Horses are bulky, temperamental bordering on psychotic, and primarily useful currently as components for high end dog food. I don't like horses. I had to hold horses while the old man did unspeakable things to them. The horses in turn attempted to do unspeakable things to me. Don't like horses. The cowboy carried a handgun, I would assert, so that he could shoot the horse on which he was mounted when it started acting psychotic. Don't like 'em.
Dogs, on the other hand, are useful critters, capable of hauling carts.
The food and poo issues are easier to manage. Dog cartage can use sidewalks rather than roadways.

Goats, too.

Horses are over-rated. Tho I would admit that the Preakness would lose something if the contestants were goats hauling sulkies.