The dogs at my barn always chase the horses around. Well, one of them does anyways. He bites at their heels when you're trying to catch them and I've done everything from screaming to throwing rocks at him to get him to back off. The last time I was at the barn, I was bringing my horse in and that stupid dog was trailing her heels. I feel the lead go tight and I was yanked suddenly. Refusing to let go, I catch my footing and look up to see what was happening, and my mare was mowing the dog down. I guess she just about had enough of him. I pulled her short of trampling him and brought her in. I doubt that broke the dog's habit but it sure made him think twice about nipping at her for the rest of the day.
I have also shot dogs with BBs. When I was in Georgia, there was a woman who would bring her horrible dog to the barn even though it would chase the horses everywhere. I finally got a little pellet gun from the store and shot him everytime he would attempt. She went haywire, but I warned her again and again what would happen if he continued. After that she stopped bringing him to the barn.
If the dogs chase the horses into a frenzy, I would get rid of them one way or another. The downside is that if you kill it and they find it, they can do stupid stuff like attempt to press charges. If you just take it to the humane society (in another county as someone suggested) then the dog will just be gone.
They might get another one to replace the lost one, but at least the first one will be gone.
And those who were seen dancing were thought to be insane by those who could not hear the music