A quite similar horse species went extinct in North America ~10,000 years ago likely due to humans.
The horse ancestor species come from the Americas and migrated to Eurasia over the bearing land bridge.
Horses were only missing from North America for 10,000 of the last 50 million years.
I was about to say the same: https://en.wikipedia.org/wiki/Evolution_of_the_horse#Equus
Of all the examples to pick from, seeing GP picked horse made me wonder if GP was doing it for gits and shiggles.
I've always had a soft spot for the plan of repopulating the Great Plains with modern versions of all the extinct megafauna. We used to have camels and cheetahs and lions and more. We could import half of the African large mammals and they would have had near species analogs in the relatively recent past, geologically speaking.