Expanding slightly from a previous answer I wrote. It only looks as far west as Indian Territory but I'll see if I can't expand more on involvement beyond there in another follow-up:

American Indians found themselves on both sides, and no sides, during the American Civil War. With numerous nations distributed not just in Indian Territory, but also Kansas, and a not negligible presence in Arkansas and Missouri as well, there proximity to the conflict made this nigh inevitable in of itself.

To start, the 'Five Civilized Tribes', who had been pushed westward by the ceaseless expansion of the United States', had in many ways adopted some aspects of the (newer) American way of life, but theirs' was a precarious and often hard existence. Forcibly removed from their ancestral lands by the white interlopers and smashed together into foreign land, much smaller than before, and crowded with numerous other alien cultures. Within and across the cultural groups, squabbles about assimilation of American ways versus maintenance of traditional lifestyles was often a major rift. Especially for the wealthiest members, their lifestyle in many ways reflected the plantation system of the American South, down to the land being tilled by enslaved black workers, but many others rejected such abandonment of their identities as Cherokee or Creek. Slavery especially could be a major point of contention, with some tribes embracing it, and others cautious or outright hostile.

Nevertheless, when war broke out, the 'Five Civilized Tribes' nominally threw their lot in with the Confederacy, although not all with the same degree of relish. The Choctaw and Chickasaw, who had taken the most to Southern style slavery, jumped at the opportunity to sever ties with the Union, while the Cherokee, Creek, and Seminoles, who had stronger abolitionist views, or at least ambivalence, less so, although in the end they too felt that cultural and economic connections with the South couldn't be overcome. Fighting units were raised, and Indian Territory prepared for war.

Decisions were hardly uniform though. Especially within the Cherokee, Creek, and Seminoles, major rifts appeared, and internal factions refused to go along, prefering to side with the Union. And of course, the 'Big Five's' decision was for many smaller groups essentially forcing the issue for those within Indian Territory, either taking the side of the Confederacy, or risking destruction. Those who did not wish to side with the South were mostly forced to flee north into Kansas, where the Union in turn took advantage of the rift to raise their own units of American Indian soldiers, a path which, as seen below, could often be a bloody one to follow.

There were several key "cleavage points" which on which we can see affiliation breakdown. One of the most interesting to note is the racial underpinnings, with "full-blooded Indians" more likely aligning themselves with the Union, and those of "mixed-blood" (by which we mean of white and Indian ancestry) with the Confederacy. This division, long-simmering before the war, was starkly represented by the Keetoowah, a Cherokee organization intended to protect their traditional way of life (although somewhat Christianized), and which saw many fight in Union Blue or with the paramilitary Jayhawkers, and the "Knights of the Golden Circle", a Masonic-esque group with several Native chapters, which appealed especially to those of mixed-race, and intermarried with whites. The "Knights" were closely associated with Stand Watie, who would gain fame as a Confederate general, and the last to surrender. Both, in their own way, promoted racialist views, with the Keetoowah concerned about outside impact on traditions, and the "Knights" promoting a pro-slavery, anti-black platform not dissimilar from the racial and class views found in the white South. During the war, Black soldiers, who were used to a good degree by the Union in campaigns there, were often given no quarter and massacred by the Confederate Indian units when offering surrender. In any case, this overall view sets the picture of Union and Confederate loyalty, with traditionalists feeling more to gain with the Union, and those of a more assimilationist bent siding with the Confederacy.

Views on race were also starkly apparent specifically within the Seminoles, who has the largest integration of African-Americans into the tribal group. As noted above, they had stronger abolitionist views, in large part due to historical intermarriage with black persons in the tribal history. African-Americans were decidedly looked down upon though by those of mixed heritage, which should be understood as White and Native, not Native and anything else, so those of mixed native and African ancestry would have likely felt more affinity with the "full-blooded" groups than the alternative. As a result the Seminoles were more strongly (although by no means entirely), leaning towards the Union in comparison to other groups, but due to tribal politics, they too were officially allied with the Confederacy.

As we'll return to shortly, Opothleyahola's desperate march north was a group of Creek and Seminoles who wanted no part of the Confederacy, and included former/escaped slaves within their ranks. They weren't the only ones either, but the most official treaty, insofar as we can say there was one, of Seminole allegiance, was negotiated with Albert Pike on behalf of the Confederacy by the Principal Chief John Jumper, but despite his title, it can hardly be said he represented his nation uniformly. The biggest cleavage within the Seminole nation was by confessional lines. Those who had converted to Baptist persuasion, led by Jumper, were of a more assimilationist bent and leaned towards the South, while Presbyterian Seminoles had stronger currents of abolitionist thought, and would follow Assistant Principal Chief John Chupco towards the Union. According to Warde, roughly half the Seminole nation followed Jumper to the Confederacy. Of the rest, it was a mix of Union-leaning, and many who would prefer to simply remain neutral and abide by the treaty requirements with the US government, although that wasn't always possible.

All in all, only the Choctaws and Chickasaws, of the "Five Civilized Tribes", saw no subfactions side with the Union, the other three fighting for both North and South. The smaller Quapaws and Senecas were the only significant nations who made no noticeable contribution to the South.

For the conflict itself, although the early clashes between Union and Confederate formations of American Indians were fought in their own, traditional styles of warfare, this was short lived on the whole. The 1861 campaign, pitting Creek and Seminole's under Opothleyahola, and loyal to the Union, against a Confederate force of mostly Cherokee and Choctaw, with support from two regiments of Texans, was in many ways more like guerilla warfare than the set-piece battles we think of for the Civil War. Both sides made ample use of ambushes, skirmish lines, flanking, and deception, and the overall tactical milieu resembled a hunting party writ-large. For Opothleyahola's forces, they included a large train with many of the warriors families in tow - fully 2/3 of the group were non-combatants - as their overall intent was to reach Kansas, and safety. The campaign essentially ended with the Battle of Chustenahlah, which saw the Union-loyal traditionalists mostly routed when their ammunition started to run out. Not just the men, but many women and children were killed by the Confederates as they were run down. The survivors reached Kansas, but Opothleyahola's group had taken grievous losses, and now had to survive the winter as well, while ill-supplied to do so. These refugee camps saw a 10 percent death rate that winter.

This question comes up frequently

Here are two excellent answers from the FAQ

This one by /u/Reedstilt https://www.reddit.com/r/AskHistorians/comments/201dtq/how_aware_were_native_american_populations_of_the/cfyxfen/

and this one by /u/The_Alaskan https://www.reddit.com/r/AskHistorians/comments/39nup4/how_did_american_indians_react_to_the_american/cs4zzez/?context=3

I’m a Texas History historian, and I think I can present to you some information relevant to this discussion.

At the time of the Civil War, the western portions of Texas (specifically the areas between the Rio Grande and the Colorado River) were still very active with Comanches and Apaches. During the 1850s, a line of forts had been established by the Federal government that essentially ran down the entire length of the state.

When Texas joined the Confederacy, the southern government seized control of these fortifications with the intention to keep them garrisoned. But, by 1862, the Confederacy realized that holding the western forts was pretty much going to be a hopeless endeavor.

Around the same time, 1862, the Comanches also realized that the Confederacy was too weak to hold the western portions of Texas. Seeing an opportunity to regain the areas that they had previously held, the Comanches started launching massive raids against the isolated settlements of the region.

The settlers were in uproar. Each raid was becoming increasingly more destructive, and the Confederacy was doing nothing to protect them.

To try and assist their people, the Texas government established Frontier Battalions and began using Texas State Troops to man and patrol the western regions. However, these units were poorly manned and had no supplies. Most of the men were even using their own weapons and wearing their own clothes.

For a time, the Frontier Battalions were doing an okay job in patrolling the western regions of Texas. But, in early 1863, the Union launched a two prong invasion of both the Rio Grande and the Texas coastline. Because of these campaigns, the Frontier Battalions were re-deployed to the Rio Grande to face the Federals...once again leaving the western settlements opened to Comanche attack.

The raids on the settlements started again, and were now even more successful than previously. By 1864, the vast majority of the western settlers had relocated to the east bank of the Colorado River, essentially surrendering their farms and ranches to the Comanches.

Since 1862, more specifically since the failure of the Sibley New Mexico Campaign, the Federals had occupied everything west of the Pecos River. By 1864, the Comanches had become emboldened by their successes against the Texas settlers, and they decided to try their luck against the Union forces in the west.

A few raids were launched against the Federal forces in New Mexico, but the attacks met with little success. In an attempt to counterattack the Native Americans, Colonel Kit Carson was dispatched on an expedition that eventually penetrated the Texas Panhandle. His forces met with great success against the Comanches at the First Battle of Adobe Walls in the November of 1864.

At the end of 1864, the Comanches had essentially regained control of the western portions of Texas that lay between the Pecos and Colorado Rivers. The settlers, by this time, were wholly disheartened with both the Confederacy and Texas governments. Both entities had failed to protect them, and even worse, had done nothing to try and recapture the western frontiers.

In early winter of 1864, a small force of Texas State Troops discovered indications of a massive number of Native Americans moving southward in the present vicinity of Abilene. Although it appeared that the trail was leading in a southwesterly direction, venturing away from the settlements along the Colorado, the Texas State Troops sent word to the settlers to be wary of a possible attack.

The report from the State Troops spread like a wildfire through the scattered settlements along the east shoreline of the Colorado River. Suddenly, the citizens were assembling militia units and volunteers to prepare for a movement against this large force of Native Americans...whom they presumed to be Comanche.

As the Texas State Troops continued to track the column of Native Americans, it became increasingly evident that the Indians seemed to be heading towards Mexico. It also started to be seen, that the force consisted of families who were also armed with military grade muskets.

The Texans continued to assume that the natives would eventually turn towards the Colorado and launch a major offensive into the settlements. Shortly before Christmas, 1864, the militias and volunteer units were called upon for assistance by the State Troops.

The volunteer units from the settlements assembled shortly after December 25, and started their march to a designated rendezvous point in present day Tom Green County. In early January, 1865, the volunteers and Texas State Troops met at Spring Creek in the western portions of Tom Green County.

On January 8th, without proper guidance or intel, the combined Texas forces (numbering about 200) launched a poorly planned attack on the Native encampment near present day Dove Creek (in Irion County).

Unbeknown to the Texans, the Indians were actually Kickapoo that had been allowed to leave a reservation in Kansas to live with their relatives along the Rio Grande. Also, unbeknown to the Texans, the Kickapoos numbered almost 200 more than the Southerners, and had been given confiscated Enfield muskets for protection against the Comanches.

The Battle of Dove Creek was a disastrous defeat for the Texan forces. Not only were the Southerners routed, completely, but one of the heaviest snowfalls in West Texas history dropped over five foot of snow on the evening of the battle.

Causality numbers for the Kickapoos have never been correctly identified. But, it is estimated that only about 10 Native Americans were killed or wounded during the fight. The Texans, however, lost around 30 men and one of the two commanding officers.

The Battle of Dove Creek was one of the largest Native American battles in Texas History. It also provoked the Kickapoo people to retaliate against the settlers, and Federal Army, in the years directly following the Civil War.

So, I guess in a summary of this very lengthy response, the Native Americans in Texas (primarily the Comanches) during the Civil War, saw the conflict as an opportunity to regain their lost territories in the western frontier of the state. The raids against the Texas settlers, during the war, fueled the flames that would eventually spark into the Indian Wars of Texas in the late 1860s, ‘70s, and early ‘80s.

Hope this adds to your research.