It may or may not have been your fault. The law classifies animals as wild or domestic. It imposes on a person who keeps a wild animal the highest duty of care to prevent it from injuring others. In some places, this is strict liability, which means if its your animal that did the injury, you're liable, no matter how careful you were. With respect to domestic animals, the law imposes only a duty of ordinary care, which often allows for the animal to injure another without you being held liable for the injury.
Horses are domestic animals.
The standard of care is due care, which means the care that a reasonable person in the same or similar circumstances would have exercised. The absence of due care is negligence. However, there remain cases of mysterious escapes. When neither side can determine how the horse escaped, each side claims victory. Depending upon what state the lawsuit is in, either side might win.