I don't know if horses are considered livestock.
Generally anywhere in the east you are going to find yourself with a whole world of headache if you start shooting dogs.
You can hold the owner liable for damages tho.
I believe west VA has some similar laws, they don't have deer dogs, but it's a lot of bear hunters. Don't know what part of WVA you will be in, but I'd recommend thinking very hard before shooting any hounds that are running thru horse pasture. Legal or not, most those guys aren't going to care about the law and I'd be willing to bet they will see it as an eye for an eye. They won't have hounds, and you won't have horses.
Bear hounds typically aren't much problem on private land, they stay to large tracts of public. Deer dogs in VA, that's a different story, the days are numbered tho.