Yes, they do come off naturally, but ask your farrier, he'll be able to remove them/cut them down. You can do it your self, but I wouldn't as if you cut too short, it can bleed!!
You can soften it with vasoline and then gently pull it away when it shows signs of seperating OR, you can ask your blacksmith to cut it away. Dont try to pull it away with force or you could end up with a bloody mess that will attract flies and co (plus it hurts