In the Canon:-Edit
Red Indians, or a race very like them, exist on the Discworld. We know because in Reaper Man, there is the case of Mrs Cake's spirit guide, One-Man-Bucket, who is an Indian in all but name and bemoans that because he was born in Ankh-Morpork, he bin denied his right to roam the wide open prairie in Howondaland with his people. So Terry, in the absence of any area of the Disc that could be called North American, has elected to put Indians here in the middle of Howondaland. Bucket would appear to have most in common with Plains Indians such as the Sioux and the Comanche - his people live in tepees, have to do with buffalo and similar creatures.
In the Pessimal Discworld:-Edit
We know Arab-like peoples occupy the north (hubwards) regions of the continent of Klatch nearest the Circle Sea. This is largely desert and scrub with fertile regions around the main rivers, such as the Djel. At the other end of the continent (rimwards) are the black tribes and a thick jungle belt. I have placed the white colony of the URH in a location analagous to our South Africa. But the bit in between the desert and the jungle belt? There is no equator on the Disc governing climate and types of dominant plant growth. What I see is a gradual progression, north-south (hubwards to rimwards) from true desert, to subsaharan, through arid scrubby greenery to a rolling grassy prairie, which then shades into forest at one extremity and jungle in the other. This central plain would then be Home to the Plains Indians, analagous to our Sioux, Crow, Comanche, Kiowa, et c. Where it shades to forest, we find the Iroquis Confederation, the Mohican, and so on; there will be coast-dwelling Indians such as Blackfeet, Pinze-Nez and Scalbie. At the opposite extemity where it bakes into desert again, in between Klatch and Kwa'zululand, would be the desert tribes of Yaqui, Navaho and Apache.
A tribe of indians who, like the D'Reg, are ever ready and eager for a fight, but who lack the virtues of the D'Reg. As with their Earthly equivalent, the Apache word for "not-an-Apache" is cognate with "to be hung up by the feet with their heads inches away from a raging fire until their brains explode". They are a thickset, hardy, short and bull-chested people, dressed in fringed deerskins, with a tradition of a very special sort of hospitality to passing travellers. Elves avoid them. Both Klatch and the Kwa'Zulu have tried to wipe them out but have only succeeded in losing large numbers of soldiers.