Instructions
Travel to Lon Lon Ranch, located on a hilltop in the center of Hyrule Field, between Hyrule Castle and Kakariko Village.
Speak to Ingo outside of the front gate of Lon Lon Ranch. Select "Ride" to pay him 10 rupees to allow you to ride a horse.
Use your Fairy Ocarina to play "Epona's Song" just as you have played various other songs to this point. With the Fairy Ocarina equipped, press "Up, Left, Right, Up, Left, Right" to call Epona. When you are standing next to Epona, press "A" to ride her.
Speak to Ingo while you riding Epona, and he will challenge you to a race.
Select "Do It" to begin the race.
Press the "A" button during the race to speed Epona up for a short time, depleting one of the carrot icons at the top of the screen. If all six carrot icons are exhausted, Epona will slow down. However, after you have not used a carrot for a few seconds, it will automatically be replenished. Use these speed boosts to keep ahead of Ingo during the race.
Win the race by completing a full lap around the ranch before Ingo does.
Speak to Ingo again after you have beat him in a horse race. He will challenge you to another horse race.
Win this second race using the same strategy you used to win the previous race. When you win the second race, Ingo will lock you and Epona inside the ranch grounds.
Gallop toward the fence on the left side of the ranch while mounted on Epona, and press "A" to apply a speed boost as you come up on the fence. Epona will jump the fence, bringing both you and her to freedom.