You can make a report to the police department. There are laws about harassment and if the dog ever does anything like kill livestock or bite a child it establishes a mode of operation and history. That alone, can make a difference in how the dog is handled. A dog that bites a child with no history is treated differently than a dog that bites a child and has a history of chasing/harassing wildlife. It also means that the court treats the owner differently. In one case the owner may not know the dog has this aggressive tendency, in the other case the owner knows and ignores it.
You can let your horse handle it. If the dog does hurt your horse you can sue them and have them handle the vet care. I have seen that done. That may not mean much if the dog is any good at his job. Lets face it, chasing your horse is just practice and the more he chases the better he gets. Which means he could really hurt your horse. It may be as easy as explaining to your neighbor how expensive equine health care is. Ie this is how much an emergency call would be. This is how much a tendon injury would cost. This is how much a lease horse of the same training/skill level would be because I have to lease a horse because your dog prevents me from using my horse in these activities. Etc.
You can shoot the dog, but that can be easier for some than for others. I spend a portion of my work day euthanizing animals and honestly don't want to kill pets in my time off. In most states, killing a dog that is chasing your livestock is protected by law. Particularly if you have an established history of communication with the owner.