I would say if dogs are in the HORSES living room, it's the DOG not the horse than needs to learn the rules.
We have seven dogs. In my vid, you can see one golden retriever being chased out. He is NOT one of our dogs - he is a stranger, and rude and ignorant of horses etiquette requirements, so while he was staying here, they did a very good job of teaching him how to be more polite and thoughtful. The other dog being chased is my young new dog who thinks that horse chase games are GREAT fun... He's had to learn to play by rules, and they don't behave as aggressively towards him as they did towards the retriever, but they do still put him in his place if he gets too crazy. Dogs can move a lot faster than hedgehogs, so they be able to learn fairly quickly what kind of proximity and attitude will be tolerated by different horses, without being in too much danger. My other dogs can all move around under the horses feet, because the horses know them, and these dogs are polite, head down, moving quietly, not aggressively, move when told to by horses.. so they can safely graze on hoof clippings and manure!
I think if you try to protect the dog from being chased by the horses, he won't learn to understand the horses language of proxemics (how close is okay, and how to understand which horse signs mean "move away a bit please".) But dogs are VERY good at learning other languages..
.. so my experience is if you give them a chance to learn the horses signals, they can understand very quickly how to adapt to living with around horses.
I have not sought the horse of bits, bridles, saddles and shackles,
But the horse of the wind, the horse of freedom, the horse of the dream. [Robert Vavra]