Think of it like this. Horses do a LOT of galloping, which is hard on the feet! Hooves are a physical ADAPTATION, so that the horses won't experience pain on their journeys. They're hard, so that the horses don't feel the ground nearly as much. Now, mountain goats travel over rough terrain, with sharp rocks and steep inclines. Again, it's really easy for them to get hurt strutting around the mountains, so they evolved hard hooves to protect their feet.
