If your horse freaks out at stuff on the road I don't think you should be on the road. It's not just a liability issue--your horse freaking out could cause injury to you and/or your horse.
You need to get your horse settled down enough to not freak. Then, as suggested by others, try to avoid riding on roads as much as possible, anyway.
'Cause, yeah, like they say, you're liable for any damage.