Great Chamois

The Mountains of the East were home to a strong and ferocious breed of Goat, closely akin to the Chamois of the Ered Nimrais and the southern Misty Mountains. The Eastern Dwarves and their more western kinsmen in the Iron Hills sometimes tamed these fiends and trained them as beasts of burden and sometimes even mounts.

See

 * Goat-Steeds
 * Great Boars of Rhûn
 * Khardh

Commentary
Tolkien's Books never mention any Dwarves riding Goats or Pigs, however dwarves riding small Horses and chamois are a traditional part of the alpine myths and fairy tales.Riding Pigs is a symbolism usually linked to celtic and norse deities such as Arduinna, Freya or Freyr.