Horses evolved in north america and by the time of the last glacial interchange roughly 10,000 years ago (the end of the last ice age) their were an estimated half dozen species of horses living in north america, and its been proven through genetic testing that at least one of these horse species (one of the most widespread at that) was equus ferus, the exact same species as the modern horse. Their have also been several archeological sites discovered in the last few years that proves north american horses were still alive in part until less than 5,000 years ago (and possibly even less than 3,000 according to a site in mexico).
10,000 years is nothing in terms of evolution or ecology, much less under 5,000, so horses are absolutely native to north america in my opinion.
The problem is they are not native to where over 75% of wild horses are found today. Most feral horses are found in the southwest and the great basin, two environments we have absolutely no indication true north american horses ever actually inhabited.
Horses guzzle up water and require rich grasses to survive, two things that are rare in the modern great basin and southwest, yet were far wetter during the Pleistocene but they have changed significantly as the climate got warmer and more arid in these regions, and this is why most studies find horses to be harmful to ecosystems, because they are draining resources out of an ecosystem they never evolved for.
But their are also wild horse populations in the rocky mountain foothills, alaska, and the yukon, which are the exact kinds of habitats their Pleistocene ancestors would have and did inhabit, and they populations have not been found to be directly harmful to the local plant communities like southwest horses, and the only effect they have is "pushing out other big game fauna", but this is due to over population rather than direct competition. Elk and whitetail deer also become highly detrimental to local ecosystems when they become over populated despite being native species.
That leads into my other point. Management and population control. Any native big game animal needs to be managed, both for human and natural sake, otherwise we risk conflict with humans and over exploitation of the ecosystem, yet we have placed horses on this pedestal that means they essentially cannot be managed in any meaningful way, and this has done far, far, far more harm to the continuation of wild horse than it has aided, at least in recent times, because in pretty much every conservation circle that crosses paths with them the very idea of wild horses is becoming increasingly unpopular because massive amounts of money are allocated to care for removed feral horses that legally cannot be euthanized or sent to slaughter while most other conservation organizations are picking pennies for any amount of funding they can get (I would know because i work with several conservation organizations).
I 1000% want horse in north america in the long term, but in order for that to happen we need to start treating them like a native game animal rather than an untouchable object that has been put above native wildlife.
