Hyrule Ranch has stopped loaning horses while they try to find a missing horse.
Where to Start the Quest
Go to Hyrule Ranch, which you can reach by going southwest from the west gate of Hyrule Castle Town. Talk to the man to the west of the building to start the quest.
How to Complete the Quest
Go west and slightly south from Hyrule Ranch to find a pond with a small island in the middle. The horse is on that island. Get on the island and create an Old Bed to the right of the horse, on the slightly lower ledge. Ride the horse onto the bed and it will automatically jump up to the upper ledge. Your horse will keep riding automatically in the direction that the horse is facing, so you don't have to hold any buttons or keep tiltint the control stick. When you want to stop your horse, tilt the control stick in the opposite direction. Press B whenever you want to dismount.
Ride from there to Hyrule Ranch, and ride up to the man that you talked to when you started the quest. There will be a cutscene.
Quest Reward
After you return the runaway horse, you can borrow any horse at the ranch for free. Horses you have dismounted from will be marked on the map.