People say when you get two hearts with your horse, you can ride it. Well..

What you have to do is, when in your barn stand next to the door (on the side of it not in front of it cause then my cow pushes me out, lol) and ring your vell, wait for your animals to go outside (i suggest you have a fence made up first) when you get outside stand next to your horse and push the X button, you should get on.

So you know when you get your barn and buy an animal, the next morning Hank says he forgot to give you something. He then gives you the rope-looking thing. Bring that into your barn, and stand in front of your horse and equip the rope thing. Press X then and the horse should make a neighing sound. Then walk the the far side of the door of the barn, and press X again, and the horse should walk out. If not, try using the rope and walk further. After the horse is outside, walk up to it's side and press X. You should jump onto it. Then just ride it around as if it was the character running, but faster.

First, the horse has to be ful size. Then use your reigns and take into your yard. Then stand next to it with nothing equipped and press X. That's it!