Awesome picture! 
Look at that majestic creature. I like the horses. They're just peacefully roaming around various fields. Then when I see some nasty Bokoblins harass some horses, I'll get angry and kill them. Leave those horses alone! I have three, and found a fourth I need to have.
My first one, just a regular horse from near the Twin Peaks (I assume that's the English name for it since I only know it as Tweelingberg), the White Horse, the black Great Horse and the fourth I found is the mythical King of the Wild (again, assuming translations here) which only appears on occasion.
So the horses can't run up cliffs, but what horse would in real life? Besides, if you move gently a horse will move over a lot more terrain and can climb much steeper hills than when you'd make it run. Ease into it, respect it, it's a live animal you know! Besides, I've found that a horse will do much more when you've maxed out your bond with it. Also, sure you could teleport anywhere, but only when you've discovered a shrine and who knows where they are in new areas and there can be plenty of distance between shrines to cover. Your horse will be your friend then.
