The only tribal group I have information on is the Sioux. Originally the Lakota were a woodland tribe living sedentary lives in the Great Lakes region, traveling mainly by canoe, and fishing provided most of their protein. They planted small crops of maize, gourds and pumpkins and built small permanent lodges. The only draft animals they employed were dogs, tying small travois made of sticks and hides to the dog's back, allowing it to drag around 100 pounds of goods.
In the mid 1600s the French began supplying the Cree, traditional enemies of the Lakota, with firearms allowing them to take the Lakota homeland when they themselves were displaced by European settlement. This forced the Lakota from their lake homes out to the Plains.
In the 1500s the Spanish had brought horses up from Mexico into the Southwest where some escaped and formed the basis of the great Mustang herds that had inhabited the Plains by the time the Lakota went westward. Royal B. Hassrick writes in "The Sioux" pages 69-70, "The exact date at which the Sioux first obtained the animal has not been determined. Certainly it was no later than1742 and probably earlier. In any event, the effect of the horse upon the Indian culture was catalytic."
"The use to which the Indians put the horse, and more particularly the manner in which the Indians adapted it to their needs, suggests the stability of their culture. The fact that they called it "sacred dog" or "mystery dog" is in itself important, because their conception of it as a kind of dog presupposed its use and value. To the Indian here was an animal able to not only do the work of dogs but also carry a rider. Men mounted on horseback could bring under their control much wider areas of land than had ever been possible."
Most of the tribes on the Plains lived sedentary lives, their culture handed down from the early Mississippian culture of Cahokia. Tribes like the Pawnee, Arikara and Mandan lived in permanent villages of hundreds of families. They owned horses,and rode them to the hunting grounds, but dismounted to hunt and never adapted the nomadic lifestyle of the horse tribes. By being tied to permanent water supplies they suffered greatly when European arrivals brought along diseases from Europe like Cholera and Typhoid. The decimation of these tribes allowed the nomadic tribes like the Lakota and Cheyenne to use their newly developed skills at hunting from horseback to push the weakened sedentary tribes from the better hunting grounds. The original inhabitants of the Black Hills, the Arikara, ended up in the Bad Lands of Dakota and the Pawnee were pushed to the sand hills of Nebraska. The proud and powerful Lakota and the other horse tribes were able to avoid many of the worse water-borne epidemics, were able to hunt Buffalo year round by following the migrating herds, and by learning to fight from horseback became powerful warriors able to take valuable hunting grounds from their sedentary rivals. This information is taken from Royal B. Hassrick's book "The Sioux".