One good example of Amerindians with horses might be Gaicurus. The moment these guys learned how to horse, it was love. They allied with a tribe of rowers with spear-paddles and then it was off to the horse races. Warrior society, raids a lot, kidnaps children to rear in the tribe. Very aggressive.
Aside from the American West, I suspect the Brazilian Northeast and Center-West (Catinga and Sertão) might become the site of horse cultures. These are very desert/steppe-like areas, generally not proper for extensive farming.
I don't think Horse cultures would work in places like the Andes or the Amazon, but having horses would definitively help them. Jungle cultures might be pretty much unnasailable by the horse cultures, because to get to them, one has to march through multiple kilometers' worth of heavy jungle. A culture like say, the Marajoaras, or the builders of Kikohugu, might as well live on a island by this standard.
I wonder if the coming of horse and the greater prosperity might lead to maritime cultures? I'm thinking native american phoenicians and greeks myself.