If horses were obligate carnivores, they probably wouldn’t have been as readily domesticated. It’s cheaper to feed a plant-eater than a meat-eater. Dogs are omnivores, for example, because human scraps are often plant-based so it was an advantage to be able to eat more plants than a wolf might have.

And if horses weren’t domesticated, that would have changed the development of technology and warfare massively. We might have still had the wheel from the potter’s wheel, but things like carts and chariots might not have developed and spread like they did if one of the main animals to pull carts was not domesticated.

The way the horse and stirrup changed warfare also would have made ancient war very different, as there’d be no sudden incursions of horse-mounted warriors invading various regions at various times so I bet a lot of national borders in the modern day would be quite different.