Easy Way To Beat The Horse Race:

Once you have Epona, go to Milk Road. Get 50 Rupies and then enter the ranch ( the first alley when you enter Milk Road). Talk to the guy standing by the fence, he will chalenge you to a race. When it comes to the part where there are fences, hit A until there is only one carrot left. Epona will soar over the fence. Also, avoid the spots that make you jump, they look helpful but slow you down.