Feral horses are a problem in the American plains and west with one of the issues being the fact their carcasses will attract grizzlies or black bears which can then encroach on humans. Hiking out, digging a massive pit, and then burying a horse really isn't an option so they blow them up to increase the speed of decomposition.
They also degrade and destroy native grassland and the whole problem could be easily solved with a cull of the herds, but some dipshit-wanabe-cowboys are obsessed with "saving" "wild" horses so now the federal government has to spend over a $100 million on horse contraception to keep the population vaguely in check.
TDLR: We blow up a bunch of horses corpses every year because of a politically connected nonprofit.
That's a good point, but from the article that you linked they had been completely absent from the continent for up to 10,000 years, until they were reintroduced by the Spanish:
Equus flourished in its North American homeland throughout the Pleistocene but then, about 10,000 to 8,000 years ago, disappeared from North and South America. Scholars have offered various explanations for this disappearance, including the emergence of devastating diseases or the arrival of human populations (which presumably hunted the horse for food).
Despite these speculations, the reasons for the demise of Equus in the New World remain uncertain. The submergence of the Bering land bridge prevented any return migration of horses from Asia, and Equus was not reintroduced into its native continent until the Spanish explorers brought horses in the early 16th century.
That's a good point, and raises a bit of a philosophical question. Horses evolved in the Americas, but were gone for a period of time. How long does an animal need to be gone from a region to longer count as native? They've definitely changed a lot, especially the domesticated version that was introduced by the Spanish.