I have recently been doing some research on 19th century depictions of American Indians, so I might be able to help. However, I think it's important from the outset to note that "American Indian" is a designation applied by outsiders (Euramericans), and not one that was used by native peoples before the relatively-recent American Indian Movement, after which it was used as a political tool by activists. American Indians then and now know themselves by their own names (Dine, Lakota, etc.), just as Europeans know themselves as Danes, Irish, etc.

So it would be inappropriate to comment generally on how "American Indians actually looked." Just like people in other parts of the world, modes of dress and person adornment would have varied based on climate, other environmental factors, and culture. The Mohawks of present-day Western New York and Ontario would have by necessity dressed very differently from the Shoshone of the Southwest or the Inka of the Andes. Further complicating this fact is the fact that American Indians, just like all people everywhere, change and changed their appearances based on new factors, such as the availability of new import goods and changes in environment. If you take anything away from my answer, it should be my exhortation to remember that American Indian societies were and are dynamic things, and there is no way of universalizing them, nor is there a way to fix them in time.

That being said, there has been some really excellent research on 19th century depictions by White Americans and Europeans of American Indians. These exact depictions changed throughout the course of the century, but there are some overriding themes. White depictions usually were interested in emphasizing the supposed 'savagery' of American Indians, usually in order to justify the belief that these 'noble savages' were not fit for the modern world, and would naturally disappear. Another frequent reason was more active - by portraying native peoples as savage brutes, it would be easier to justify their extermination. So whether the purpose was ethnological or propagandistic, the depictions emphasized the strangeness of these people in White eyes. When Native people tried to wear White clothes or otherwise ape Europeans, they were frequently ridiculed for, in essence, 'doing it wrong.' (This is common in contemporary depictions of African American people, as well).

For an example, see the painter George Catlin's portraits of American Indian people. Undoubtedly these people were wearing their own clothes, but Catlin also emphasized their strangeness, as did Carl Bodmer, a Swiss artist-traveler, also of the antebellum period. [This painting] (https://upload.wikimedia.org/wikipedia/commons/b/b2/George_Catlin_-Wi-j%C3%BAn-jon%2C_Pigeon%27s_Egg_Head%28The_Light%29_Going_To_and_Returning_From_Washington_-_Google_Art_Project.jpg) by Catlin shows nicely how Indians could not win either way, being ridiculed for their strangeness but also for their inability to properly mimic Whiteness. As you will see from looking at works by Catlin and Bodmer, as well as other artistic and photographic depictions of the time, many American Indians did wear their hair long and/or bald and/or elaborately-styled, and some did wear fewer clothes than White people were accustomed to. However, most of the American climate is temperate, so going mostly bare for much of the year was just not practical, just as it is not now.

I hope this has been some help - it is a subject that is hard to speak generally on. I guess the takeaway is that individual depictions might be termed "accurate," but the ideological thrust of such depictions was towards Othering Native peoples in order to justify their removal and slaughter.

Sources:

Deloria, Playing Indian Berkhofer, The White Man's Indian Truettner, Painting Indians and Building Empires