They obviously could have used horses. Indians wistfully looked over the plains atop their horses, until the white man came and ruined it all. At least that is what Sedona tourist art leads me to believe.
Horses didn’t exist in Western Hemisphere until the Spanish brought them over. Horses were once native, but they died out at the end of the last glaciation. The closest thing to a horse in the Western Hemisphere was the camel cousin - the llama!