In The Legend of Zelda: Ocarina of Time, the horse Link can ride is named Epona.
Link first encounters Epona as a young boy at Lon Lon Ranch, where she is initially shy and wary of people. Malon teaches Link “Epona’s Song,” which lets him form a bond with the horse. When Link returns as an adult, he wins Epona back from the ranch’s owner, Ingo, and she becomes his trusted mount.
Epona is more than a faster way to cross Hyrule Field. She lets Link travel quickly, jump over certain obstacles, and use a bow while riding. Her name comes from Epona, a Celtic and Gallo-Roman goddess associated with horses and fertility.
The other options are important characters but not Link’s horse: Zelda is Hyrule’s princess, Navi is Link’s fairy companion, and Malon is the ranch girl who helps him obtain Epona. Epona later appears in several other Zelda games, though each game’s version has its own story context.