Dogs and horses have completely different mindsets. Both need an alpha and a herd/pack, but one is a predator and the other is prey. They think quite differently in terms of food, safety, and companionship.
I think this personifies (applies human feelings, thinking, and personality to something not human) horses to much, which is dangerous (both to horses and dogs). If I treated my horses like I treated my dogs, I'm sure I'd have a hoof in my gut somewhere along the line. A horse most certainly would not put up with that level of rough housing.
This applys to a dog much more heavily, and probably should, because a dog will actually modify it's behavior to be like it's owner/alpha. And this modification, this copying of behavior, is why dogs are endeared to so well. It is genetically ingrained in them to do this, and how they have survived as a species next to humans. They depend and endear themselves so thoroughly. A horse does not do this, and mistaking a horses behavior can cost you your life.