Make friends with Animal Control. Check your local laws for the keeping of Stallions, and if anything happens, threaten with legal action. Our idiot neighbor's stud broke through our fence and tried to get with a customer's mare and foal (mare would have killed him but that is besides the point), and after calling Animal Control and having him explain the threat of suing and other legal actions, she learned that point real quick. Didn't learn much else, but she learned that.
The next time you see the horse tangled in the fence, tied, hung from a tree, loose on the road or when the enevitable halter sores form, call Animal Control and let them deal with it. Cuss an official, how 'bout cha? Cussing a neighbor is one thing, but she won't be able to ignore a man who can cite you. Or call the owner and tell them if that horse damages YOUR fence, you have pictures(might want to take some pictures if you can) and they are going to have to pay for any damage that horse causes.
Or if you HAVE to do something, say the horse has caught the halter on your fence again and you feel compelled to help, cut the dang halter and make it look like it broke. Or take it off and leave it where it was. If you feel the need to meddle and take the halters off the standing horses not tangled, take them off and drop them in the field. Make it look like the horse did it himself. I had to "help" one of our neighbor's horses who's blanket was all torn up, and pretty much tangled in his legs(a passerby stopped and asked me to go look, else I would not have). I took it off, and left it where it fell. And DON'T let them see you.
I personally don't think you should care much for the neighbor's horses, unless it is your property that is being damaged(sounded like the fence could have been in peril), then let them make their own mistakes. You can't train these people, because they obviously don't want to be trained. And you have already made yourself out as the bad guy, so LET THEM FALL. I wouldn't care less if our neighbors came and shot all their horses where they stood, just so long as the noise didn't upset our mares. Their property, their horses, their business.