I know what you mean, because of those 3 species, dogs are the only ones to be commonly kept as pets. But what is it that puts horses, dogs, and cows in the same/different categories?
I would say a dog being a carnivore puts it in a different category. The same reason I wouldn't want to eat a wolf or a big cat.
This is actually a really good point. Dogs will eat really disgusting food, perusing the trash or eating poop at times.. I wouldn’t eat a raccoon for the same reason. Horses and cattle eat grass, they’re vegan
The bigger issue is that toxins concentrate in carnivores in a way that they do not in herbivores.