Runaway Horse Side Quests

The horse can be found on a small island seen in the screenshots below.

Reward:
Can borrow horses from Hyrule Ranch

Hyrule Ranch is missing a horse. You were asked to bring her back. Apparently, she normally gallops around west of the ranch.

You brought the missing horse back to the ranch! As a reward, the ranch will loan out horses to you for free.

X: 5660 Y: 8016

Given by the old man in the ranch. The horse can be found on the small island to the south-west.