What is our recourse for damage caused to our property by neighbor's horses?
Our neighbors have 6 horses that escape their fenced in area (barb wire only) at least once every 2 months. They have ruined our yard, leaving up to 6 inch deep hoof prints that could easily cause personal injury to anyone walking in our yard.
If you can prove that it was in fact your neighbors' horses (photographs or video clearly showing the horses and the location would be ideal), I'd suggest hiring a reputable landscaper to repair your lawn, and send your neighbor the bill. If they don't pay it, and you don't care what they think of you, you should be able to sue them for this.
The owners of animals are responsible for the damage done if the animals are negligently allowed to escape. The frequency of escape, in this case, might well prove negligence in and of itself, because the neighbor has to have known by now that his fencing was inadequate for his horses.