There is speculation that the Young Dryas event over 11,000 years may have caused the extinction of horses in the Americas. Considering that Europe and Asia still had horses whose domestication revolutionized warfare, commerce, and communication among communities, would Indigenous societies have been more advanced upon the arrival of colonists had they still had horses?
The correlation between the Terminal Pleistocene, extensive human migration, and extinction of megafauna on every continent but Africa has led to a tug-of-war among researchers over whether it was the climate that caused both human migration and megafauna extinction, or humans migrating because of the climate that hunted megafauna to extinction.
Fans of the latter, the Overkill Hypothesis, point out that animals unaccustomed to newly arrived humans would be at a steep disadvantage in terms of self defence. Something very much like that actually happened in the Galapagos, where creatures like the dodo allowed humans to walk right up to them.
In the Americas, humans definitely arrived while horses were still around, but most evidence suggests they didn't try to domesticate them. They treated them like any other ungulate, hunting and eating them. (Remember that these folks arrived thousands of years before horses were domesticated anyplace on Earth.) Their descendants would eventually domesticate corn, beans, squash, turkeys, llamas and alpacas, potatoes, dogs, and a few other things--but horses were long-gone by then.
One source: https://popular-archaeology.com/article/horse-and-camel-hunting-by-prehistoric-humans-in-north-america/
Another: https://www.horsetalk.co.nz/2016/09/29/earliest-south-american-people-ate-horse-meat/