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.
This necessarily leads to juxtapositions of peoples which simply never happened on Roundworld. For instance, the Latoka Sioux find themselves making alliance with the D'Regs against incursions from proud Klatch to their hubwards. The Apache , out in the desert, find themselves with Klatch to their immediate Hubwards and Kwa'Zululand to their rimwards: they are a thorn in the side of both. Then the URH attempted to invade and extend their country into the Indian lands, leading to war with the white man.
The Indians are generally peaceable people leading a simple pastoral and nomadic existence. Although they have long memories,they do not bear grudges, and believe in burying the hatchet over an argument. This is usually because it is buried so deeply in the enemy's skull that there is no alternative to interring it with him.
After the warlike Boors were defeated and thrown out of the Central Plains following General Rjuster's shattering failure at the Little Big Horn, the various neighbours of the Indians agreed to renounce any territorial claims to the Central Plains. The Treaty of Ankh-Morpork (1904) saw Klatch, Kwa'Zululand and the URH recognise the sovereign rights of the Central Plains Indians to their own lands which would be reserved for them in perpetuity. These days, some Indians attend the Assassins' Guild School in Ankh-Morpork, while diplomatic missions are maintained in the capital cities of the great Powers.
The Red Indians appear in these stories
* Small medium, large problem;
* Rincewind Among The Redskins