There used to be all kinds of weird wild animals in the Americas, not so very long ago, if you think like a paleontologist. Mammoths, mastodons, horses, giant sloths, camels, unicorns, and griffins are all well represented in the fossil record. Then they went away: looks as if the Injuns ate ’em.
But we don’t really know that they all went extinct ten thousand years ago: the fossil record is not that complete. What we do know is that at minimum they became much rarer. Most really did go extinct somewhere between then and now: I’m sure that there’s no longer any place for giant ground sloths to hide [or run].
But imagine that a few wild horses survived the Clovis holocaust – hanging on in places like northern Nevada, in low numbers. Indians kept them from recovering much. Not much of a fossil record, and you’d have to C-14 date them to notice that they’re anomalously young ( from a time where they shouldn’t exist).
Later, the Spanish show up, with domesticated horses. Some get into the hands of Indians, some go feral – but all are genetically domesticated, readily tameable. And the Indians now know that horses can be ridden, something that apparently never occurred to their hunting ancestors. At the same time, wild horse herds are increasing, since Amerindian populations are collapsing from Old World diseases.
If there were any remnant herds of ancestral North American horses, they mixed with Spanish-origin feral horses. Probably the Spanish-origin horses would have done better, accounted for most mustang ancestry, just as Old World dogs largely replaced Amerindian dogs. Better pathogen resistance, likely.
Still, American mustangs might still have a touch of archaic North American horse ancestry – unlike any Eurasian horses, perhaps – just as Eurasian humans have a touch of Neanderthal ancestry, people from PNG have some Denisovan ancestry, and brown bears in Europe have some cave bear ancestry.
You might see something like this.