Firstly, as mentioned, you are liable if your horse is running loose and someone strikes it with their car. However, if your friend had caught the horse and was leading it and the horse was clearly under control, then I can't see how you would be liable.
If this guy struck your horse hard enough to kill it, did he not have sufficient damage to his car? I would think he would have put in an insurance claim for his car (which should have been declined since he was under the influence). In Alberta, we have two years to file an insurance claim. I work in auto insurance, however if might be worth looking into whether you could file a claim for property damage.
Might be kind of difficult to prove the guy was drunk driving when this occurred over a year ago, but if he hit something else in the same night.....you might have something to go on.
I would contact your insurance company or broker that handles your farm/property insurance. If they are knowledgeable enough they will be able to tell you whether you can still open a claim for your horse (this is under the assumption that the horse was covered under your home/farm/property policy). If it wasn't then your other choice is to talk to a lawyer.
Best of luck.