For a similar comparison, wild horses do surprisingly well in some desert regions of the Southwest US. It's a surprising treat to see a healthy herd of horses meandering through Joshua Trees. They can apparently do pretty well on sparse grasses and shrubs.
Those horse populations do well enough that the BLM regularly kills some off to limit the numbers. Ostensibly it's to protect the environment, but given the number of legal and illegal cattle that's allowed to graze on those same public lands I think the culling is mostly at the behest of ranchers.
"Do surprisingly well" depends on your expectations I guess. Yes, it can be a treat to see a healthy herd. It's much less a treat to see emaciated, dehydrated horses, which are not that uncommon:
and while one can argue about the "true" motivations of the people arguing for culling/control, it's absolute true that conservation organizations think that feral horses are bad for the environment:
Wild horses in North America are a very interesting question.
All equids evolved in North America. For tens of millions of years they were here, and only have been gone for ~10,000 years until being reintroduced by the spanish. [1]
[1] See the fantastic book "Twilight of the Mammoths"
Those horse populations do well enough that the BLM regularly kills some off to limit the numbers. Ostensibly it's to protect the environment, but given the number of legal and illegal cattle that's allowed to graze on those same public lands I think the culling is mostly at the behest of ranchers.