Well there is a way to cheat but it isn't 100% right all the time. First save before going to the festival, then go to the festival and remeber who wins then reset your DS and bet on the horses that won last time. Again this isn't always right but it will sometimes.
You're mostly guaranteed to win if you bet on the horse with the lowest payout (odds). Underdogs, whoot! But if you want, the above method works well too. If you have the money, you can also just bet on all the horses (though not advised if you're trying to make money).
I don't know if it's simply a glitch in my game, but I'm able to bet on the third horse, always, and when you go on as if you were playing the horse, like in FoMT. Like, you hit the button and everything. When I do this, I always win, no joke. It's always the third horse, so long as you're pacing yourself, as if the heart is there even if you don't see it at all.