Tom Bombadil's pony who is "larger, stronger, fatter (and older)" than Merry Brandybuck's ponies. Ol' Fatty keeps the ponies out of trouble when the hobbits wander into the barrow-downs. However, there's no Fatty to save them from the Watcher of Moria, and there Samwise Gamgee loses his best buddy next to Frodo, Bill the pony.
Fatty appears in
The Fellowship of the Ring.