Once the Native Americans killed off the horse, there was no North American animal that was ridable! Old World people had the horse and the donkey.
South Americans had the llama, which was domesticated but not readily ridable.
But the Spaniards inadvertently gave horseback riding back to the Native Americans!
Horses migrated off the North American Continent about 2 to 3 million years ago. They were reintroduced here when the Spanish arrived.
Once the Native Americans killed off the horse,
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NA horses were killed off in the same cataclysm that killed the mega fauna - Nates had nothing to do with it.