Keep Your Horses
If you find a horse out in the wild, try to tame it. You can tame a horse by sneaking up from behind and mounting it. All you have to do is hang on to it until the horse calms down. However, simply taming a horse won’t make it yours to keep permanently. You have to go through a simple process to properly own the horse and give it a name.
Once you’ve unlocked the main region of Hyrule, you’ll be able to find stables all around the world. While on horseback, ride it to the nearest stable you can find. For the small fee of 20 rupees, you can buy a saddle for the horse and even give it a unique name. From here on out, you’ll be able to whistle and call the horse to your location just by pressing down on the d-pad. If it’s within earshot, of course.