Domestication of the horse happened twice. Once somewhere in Asia and the second was on the plains of North America in the 1500s-1600s.
Your statement surprises me.
Horses lived in North America a very long time ago, but the Native Americans found them tasty and hunted them into extinction. Then there were no horses in North America. Until the Spanish arrived with their domesticated horses. Some of which were stolen and some of which escaped. That’s how Native Americans got hold of domesticated horses.
I’m not at all sure that Native Americans deserve credit for domesticating horses on the plains of North America in the 1500s-1600s