All of them has a somewhat a connection to the animals, except piGrass and TT-beaver. Condor is part of El's name, King penguin, squirrels store food (though not in its stomach like Spe did), and Seiun is a cat in all but species.
The real horse Grass Wonder has a reputation as a keen eater. He always has a great appetite and actually weights more than Special Week throughout his career. It was said he spent most of his time eating, sleeping and standing still in his retirement. So people referring him as a pig. (but out of love, no bad intentions)