There is a myth that dogs and horses (predator and prey) are incapable of cohabitating. The same would have to apply to sheep and herding dogs and even dogs protecting chickens. Without clear training and the proper default behavior the results can be bad. Even when training the horse with movement- the canine can be trained to assist by observing and not participating.
Chasing horses, barking at horses, lunging, nipping, and running under horses are all behaviors that can get your horse and dog (possibly a rider) hurt or worse. The energy of the dog when doing this is high and excited- causing the horse to respond. What happens when the dog is given direction to use a calm behavior as a default? How do you think the horse will respond?
Dog World trainers can change a canine's behavior, and we have a horse trainer on staff that can help in both worlds. We will create a program that will give you a pack with calm behavior, and you the tools to maintain. this is not a magic bullet but is easily understood by horse people.