I am not a lawyer, but grew up with my father's legal business, so take what I say with a grain of salt. I would consult a lawyer to see what the local laws about property damage entail, as they can greatly differ from place to place.
Did you file a police report when the horse was killed? How do you know it was the same man if he did a hit and run the first time?
Unfortunately, time is of the essence when dealing with legal matters. If you can prove that this man killed your horse (which, since there was presumably only one witness, may be next to impossible at this point), you could request his insurance information and file a claim for property damage. Livestock and pets are considered property under most jurisdictions. Sadly, a year is usually too long to wait to file for property damages.
If you can provide proof that this man killed your horse (police report), and proof of his value, as well as a receipt for euthanasia, vet bills, carcass disposal, backhoe rental, or any other costs you incurred, you can take it to a lawyer and see if you would still be able to take the man to civil/small claims court.
To give an honest opinion, unless the horse was valuable or you incurred significant costs (Over $1000+), taking the man to court may be more trouble than it is worth. Besides court costs, time away from your job and gas, suing someone can be expensive. You may get a judgement against him where the court orders him to pay, but you still have to get him to pay - which may involve retaining a lawyer, having a sheriff or process server serve him with notice of the judgement, and then having that lawyer assist with freezing his assets or otherwise.
Weigh the costs carefully against the potential gain, and definitely speak to a lawyer. Many will offer a free 30-minute consultation to look over your case.