I didn't read the whole thread, but I have ponied my dogs from my horse successfully. I used to board somewhere with a lot of back roads to ride, and I would bring the dog along for exercise too, ponying alongside my horse with a horse lead rope. Of course, the dog has to be 100% obedient, calm, and not fearful. The horse has to be experienced at ponying other horses reliably and good with dogs running next to them and near their legs. My horse had foxhunted and trail rides with dogs off leash a lot, so she was fine.
Now I use an e collar (Dogtra with 1 mile range) and ride with my dog off leash. I do carry an extra leadrope in case I have to put a real leash on the dog at any point and pony. My current young heeler knows how to safely ride the horse too, if needed. (seriously- he can even jump up there himself, sits in front of the rider quietly, even on steep/technical terrain. I don't trust my horse 100% but hubby's ranch bred paint is so calm and does perfectly with the canine rider)