Your dog would not mind eating your horse. Your dog also wouldn't mind eating you.
There's two principal reasons why people make a difference between cats/dogs on the one side and horses on the other: The degree to which they're family, but very crucially also to the degree to which horses, or cows, very much aren't carnivores, it's about position on the foodchain, how much heavy metals etc. accumulate, that's not just a modern thing it's always been the case. That's why eating dogs is an exception among human cultures, while with cows not eating them is the exception.