It's a bit much to cover here, but you might like to get in touch with some people who do field trials with horses (vs the strickly dog field trials). Of course you would be looking at just the training portion that involved training the horses and dogs working together and not the competition training that is mostly for the dogs.
Dogs and horse can do quite well together. The only problem I've had so far was years ago I had a Malamute that could be very agressive towards other dogs (he wanted to be the alpha male for ever canine alive). Holding him on a lead was difficult then. I over came it by teaching him to jump into the saddle with me so I could keep him there until we had passed any dogs we encountered. It was a bit much and my QH was the only one I could ride with him, since the other horses wouldn't deal with him jumping up into the saddle.
Other dogs I've had did well and would basically heel along side the horse as if we were taking a walk, but I kept them on a lead unless we were just riding around the farm.
And of course there's the potential problem that's already been mentioned for when other dogs are encountered and how they will act. You can't always just trot off, since they will often follow. Things are seldom easy.