Your horse getting out and getting hit doesnt automatically make you liable for the vehicle damages. That is false info that keeps popping up on this thread. Lots of other things are involved like the condition of your fence. Negligence has to be proved. SOme states you arnt required to even have a fence.
If a drunk hit my horse in the road I would be calling the cops ASAP, if he was drunk enough to hit a horse he was drunk enough to kill someone and shouldnt be driving at all. Most likely they would have had to pay all the bill any way.
If you are actually riding the horse on a road in VA, if you have a refelective vest on, cars are required by law to maintain a certain distance, so you'd have to pull out in front of them basically. Not sure how that would alll pan out in liability issues. Seriously though based on what I have found out if you have horses on you property or anything remotely considered as being a farm, or even just a ferw acres you need to see a company that sells farm policies instead of homeowners.
The reason horse liability insurance is so cheap is because there are very few and extreme circumstances where you are held liable.
For instance if your horse kicks a car in an area a reasonable person would expect a horse to be, like a fair, or a trail head parking area. That would be a claim on the owners comprehension same as if a tree fell on it.
If you are on a horse in an area with big signs up that say NO HORSES and it kicks a car you may be held liable. At least in VA, like I said other states may be different.