I would find a good hiding spot near there to make sure it is not a bear. You know that they keep bears from breaking into cabins by taking a piece of plywood and putting nails or screws through it. Then placing it where they don't want bears to go. The bear steps on it and learns not to go there. That would be completely illegal to put something like that out for people. It may work for raccoons too

I think a little rubber or plastic around the gate where the chain goes and then hook hot wire up to the chain. Any man or beast will touch the gate when grabbing the chain. Then you take video from the camera and send it in to the video shows to help pay for the vet bills.
For real I would not try to run them off. I would catch that *&%#$ and they would be paying for the damage to the horses. If they let the dog go it sounds like some crazy animal rights person or just some stupid kid. Either way they should learn a lesson and you should be compensated for your loss.