It really depends on the laws in any area. Drunk driving is an offense in itself, as would leaving the scene of an accident be. I heard of someone who was charged with driving under the influence, reckless driving, and hit and run because the police had a good description and his license plate #, and when they contacted the man at his home he was still above the blood alcohol level, and there was evidence of the accident on his truck. The OP's case might be different because it may have taken time to figure out who the man was. The horse did get loose, but at the time of the accident it had been caught and again it depends on the area because in rural areas livestock seem to get better consideration. If there was a good enough case against this man that he did hit and kill the horse, I would think his insurance (if he had insurance) would cover it as damage to property..