Liability for accident?

I doubt it.  If the person is already in contact with your insurance company, you don't really need to worry about this, because the insurer's attorneys will deal with this.

Dogs bark.  It isn't negligence if your dog barks, and it isn't your fault, or your dog's, if that spooked the horse.  It is possible that there was negligence because of the leash, but that would have to be proved, for example by showing that the leash was already worn out or torn, or too light for your dog's weight.

In many states, the law holds a dog's owner automatically liable if the animal bites someone.  But that kind of statute doesn't get extended to this sort of fact pattern.