I agree with most of what Shags said. I would however add this caution...
A horse can kill a dog with a single blow, especially if it is shod. I have seen it. 'Nuff said.
My first horse was a gem around dogs. I am sure that this was becasue he was trained and conditioned by his previous owner and also by a dog pro who kept my horse for me, for most of the first year I owned him.
When I got my second horse, I discovered that he was not as forgiving around dogs as he appeared to be at first. He raised his front foot a cvouple of times and kicked out slowly
around a very mellow older dog. I decided that was not going to be tolerated...at all... and I began disciplining the horse for reacting in any way shape or form to a dog in its vicinity.
I deliberately conditioned the horse by(among other things) bringing a dog, with me in between, right up next to the horse and eventually took the dog which was standing on its back legs with its front paws on my chest and placed its front paws on the horse. Positive reinforcement for both dog and horse here.
Eventually, I permitted the horse to swing its head around and look at and even nuzzle the dog... again with positive reinforcement. The first time the nuzzle turned into a bite, I disciplined. It stopped.
He eventually learned to accept dogs in his close proximity and understood clearly that it was a major part of his job to look out for them, especially when roading.
You will know you got a dog horse when you are roading a brace of dogs and the horse stops short, almost thowing you over its neck because one of the dogs stopped to pee ...and of course, you weren't paying attention.