The mountain goats are seen in one of the last scenes of the episode "Hug Wolf." There are multiple goats standing on various hills while Hug Wolf Finn and the Alpha Hug Wolf hug each other some distance away from the goats. As the two continue hugging, they cure themselves, which results in a large heart-shaped blast. This giant blast is strong enough to blow all of the goats off the hills.
The goats all are like normal goats. They have long curled horns and white fur.