I knew there were Native American reenactors -- in Germany, that is.
I was unfortunately ignorant of these reenactors in the US, until I watched a dance demo by some reenactor (and actual) Cherokees at an event in Maggie Valley, NC. Not the fancy feathered-up Cherokees that every area tourist sees, but the real, researched McCoy. They based their impression on the tribe as it existed in the late 1700's, and it was a treat to watch them. Authentic from head to toe, these guys not only looked intimidating, they knew their impressions.
When I was doing my research, the first site that popped up (via Reenator.net) was the Woodland Confederacy. They are based in the northeast, and have a great site to check out. Their time period seems to be the French and Indian Wars, give or take a decade around those years. The Gallery is one of the first places to look at. These guys looks great, and have done the research to insure the integrity of their impressions.
Another site that is interesting is the Eastern Woodland Trekkers. I'm not really sure if they do any historical events, or if they keep within their own group, but I think I need to join their mailing list to find out! Wingeohkwet the Webmaster also has an interesting fictional account of his persona. The Eastern Woodland Trekkers are part of a larger organization, The Coalition of Historical Trekkers, that seems to be an authenticity-based derivitive of mountain man reenacting or "buckskinning".
Mahkemakwa is an individual reenactor who does the same tribe as Wingeohkwet; the Lenape tribe of the colonial northeast. Although spartan, like the other site, it does have some character and soothing native instrumental music. Link to Mahkemakwa.
This type of reenacting has a strong appeal to many people, including myself. Events aren't always centered around a battle or historical event, but probably more hands-on than most other periods.