Did it slow down settling in the "Wild West"? In relation to this question: How did the war effect immigration from Europe?
It immediately slowed down settlement, but wartime events paved the way for a massive surge in emigration once the war ended.
Migration over the Oregon Trail to California and the West Coast in general dropped to no more than 5,000 in 1861, the first year of the war. Some of those 5,000 were bound for new goldfields near Denver, but the majority headed to California (not Oregon; there were reported Indian raids on the trail beyond Fort Hall).
On Oct. 24, 1861, the westbound and eastbound transcontinental telegraph crews connected their lines at Salt Lake City. Stephen J. Field, chief justice of California, sent the first telegram, directing it to President Lincoln. In part, he said: "The people of California desire to congratulate you upon the completion of the great work. They believe that it will be the means of strengthening the attachment which binds both the East and West of the Union, and they desire ... to express their loyalty to the Union and their determination to stand by its Government on this, its day of trial."
The American military was concentrated in the West, where it occupied forts designed to protect the emigrant trails. Ultimately, 313 Army officers in the West ─ almost a third of all officers in the U.S. Army ─ resigned to join the Confederacy.
At Fort Kearny, most soldiers were Southern sympathizers, and everyone tended to gather around the post telegraph office in their downtime, awaiting the latest news from the East. When Col. Dixon Miles was ordered east with the 2nd U.S. Infantry, a Capt. Tyler was given temporary command of the fort. He immediately spiked 15 cannon ─ nearly causing a mutiny among the Union loyalists in the garrison ─ and went south to join the Confederacy.
With deserters and regular soldiers leaving the West in large numbers, territorial and state governments formed volunteer regiments to take their place. Before the war, the Mormon settlers in Utah had needed a military expedition to remind them that they were still in the United States. In 1862, President Lincoln telegraphed Brigham Young, asking him if he could supply volunteers to provide temporary protection for the U.S. mail stages and the telegraph line. Young did so, sending more than 100 volunteers to patrol the area near Independence Rock until the Sixth Ohio Volunteer Cavalry arrived.
There was a gap between the departure of the regulars and the arrival of the volunteers. In what is now Wyoming, the Shohone Indians raided and burned stage stations, attached stagecoaches, killed drivers and drove livestock away. The U.S. government ordered mail sent by sea until the situation calmed and the action shut down many of the stage lines that ran through the area.
The Butterfield Overland Stage Company, one of the largest stagecoach lines, had to stop operating in June 1861 because it used the southern routes through Arkansas and Texas, which were no longer viable. In its wake came the Overland Stage Line, which competed successfully with the other stage lines because Overland's route ─ along the modern route of I-80 and the Union Pacific for portions ─ avoided hostile Indians and the Confederacy.
Between 1862 and 1868, about 20,000 emigrants followed the Overland route, which became known as the Overland Trail. Many of these travelers were bound for new goldfields in eastern Oregon and what is now southwest Montana and Idaho.
This invasion caused Indian uprisings in the area, and volunteers from Oregon and Washington were initially unable to stop these. Simultaneously, the Sioux rebellion in Minnesota was providing an example that would be followed elsewhere across the West.
While these attacks had a big impact on travelers on the trail during the war (routes were blocked, extra precautions had to be made), the biggest impact on the West was made in Washington, D.C. In 1862, the Homestead Act passed Congress and was signed into law by President Lincoln. The same summer, Congress enacted legislation providing for construction of a transcontinental railroad from Omaha to Sacramento.
These two legislative actions, made possible because of the withdrawal of Southern lawmakers from Congress, did more to shape the settlement of the West than anything actually happening in the West during the war.
I suggest reading David Dary's The Oregon Trail for a good picture of settlement before the war, and Alvin Josephy Jr.'s The Civil War in the American West for a depiction of the "intolerance and brutality" of the U.S. government toward American Indians during the war.