If you are tribal enrolled, you do not need a license to hunt on ANY tribal land, regardless of what tribe it is. All you need is land owner permission. I am Oglala/Brule Sioux (out of South Dakota) and I hunt Cheyene/Arapaho land yearly.
You can also take out of season, but most of the time I hunt using DOW rules just without a license. My tribal enrollment card was from when I was 10. Gotta drive to Rosebud, SD to have a new one made so I usually just carry my DoIB.