From Zelda Legends Wiki
Epona is the name of Link's horse in Ocarina of Time, Majora's Mask, and Four Swords Adventures. She was raised at Lon Lon Ranch by Malon and was won by Link in a horse race against Ingo. She can be summoned at any time by using Epona's Song.
The horse Link owns in the cartoon series is named Catherine, and the horse in the upcoming Twilight Princess can be named by the player.
Epona is also the name of a Celtic Goddess of Horses. (See Wikipedia)