The Five Civilized Tribes joined the Confederacy which is why I imagined Oklahoma being split into 2 different states (Lincoln and Sequoyah).
The Quallatown Cherokee of NC also supported the CSA, mostly out of loyalty to their white Chief Will Thomas (they really had nothing to gain and everything to lose from picking a side). They suffered badly for it during and after the war iOTL. Hypothetically if they support Reconstruction (perhaps Chief Will's collapse into insanity per OTL spurs something? Possible PoD here?) they can carve out some support in their mountain enclave. Hypothetically they could be a bridge between Ex-CS Carolinians and the Freedmen.
Virginia's Indians found themselves on the wrong side of Jim Crow OTL when they were labelled "Colored" and treated the same as Blacks. Hilariously, since the "one drop" rule was in effect, many of Virginia's First Families, who claimed ancestry through John Rolfe and Pocahontas, were suddenly "Colored" by law, and a special "Pocahontas Law" had to be passed to prevent the state's elite from having to sit in the Colored section! In this case, Virginia's Indians would benefit in the long run from a successful Reconstruction simply by avoiding Jim Crow.
Sequoyah could eventually, I assume, use the courts to win rights and redress grievance.
Out West the "Uncivilized Tribes" will face a much harder time. Hard to imagine how they arrange anything better at first. The Sioux are likely to go to war with the US per OTL as two aggressive military empires can't coexist. Ditto the Comanche and certain Apache and the other Plains Nations. Perhaps the Osage and any Nations that partner with the US fair better? That said, I could see the more "Civilized" Puebloan cultures and the Navajo eventually following Sequoyah's lead, perhaps some Californian or Oregonian/Washingtonian/Alaskan nations as well.
So, in the near term "not good", but perhaps in the longer run they could use the precedent of the Freemen to gain more rights and perhaps avoid some of the worst abuses of the late 19th/Early 20th centuries (e.g. the Reservation Systems and Indian Schools).