On the subject of early english colonists,
Mail armor was mostly considered obsolete in western europe at this time but the short answer is that yes, the colonists did use mail along with brigandines, buff coats, and various padded armor at times. The most notable example would probably be right after 1622 massacre at Jamestown. The crown agreed to collect various arms and armor from the tower of london which had grown old and "unfitt for any moderne service here" and ship it to Virginia. This included 2000 "skulls of iron", 100 brigandines, 40 plate coats, and 400 shirts and coats of mail. That same year Edward Waterhouse wrote that "Prospective colonists were advised to bring with them. . . suit of light armor (one for every two men is enough)." A census of arms in Virginia a couple of years later recorded out of 1209 settlers 342 "armor complete", 206 "coats of mail and headpeices", 20 "quilted coats and buff coats", and 26 "jackets, jack coats and corslets."
Even as late as 1644, militia in Virginia were being ordered to wear "some defensive coat or armor and a head piece" on campaign. Even during this period though, officials apparently had trouble getting men to wear their armor often enough to get used to the weight and there are multiple examples of soldiers being ambushed and unable to use their armor since they had left it sitting in a wagon or a boat. On the other hand lack of armor was not necessarily a death sentence, the settler's firearms outranged the americans' bows and could be reloaded from cover. Unlike a bullet, an arrow travels relatively slowly, and if shot from too far away an attentive militiaman might have time to dodge or duck behind a tree. Furthermore arrows tended to be less fatal than high velocity bullets. Compared to Virginia, the Plymouth colonists weren't nearly as well equipped, and relatively few of them wore armor. During the Pequot war John Mason and John underhill recorded a high number of wounded over the course of their campaign, but fairly few deaths.
In either case, by the second half of the 17th century natives on the east coast had become fairly well equipped with firearms from trade and there was little reason to use armor any longer.
Arms and armor in colonial America by Harold L. Peterson
Is there a source you have that says the chainmail used by conquistadors was effective against Indian projectiles? In 'American Indian Archery" by Reginald Laubin, he mentions that chainmail wasn't nearly as effective at defending against Indian arrows as indigenous forms of armor (such as cotton and hide).
Just a small point in regards to late 1800s US cavalry. By that point, large numbers of rifles were in the possession of natives. Combine that with the way US cavalry was used at that point (more as mounted infantry rather than shock cavalry) and it becomes clear as to why they weren't using armor.