Here are a few hints I thought beginners would really need to learn:
To Gallop, press the square button while pushing the joystick forward.
You can also get a good leaping start by simply pressing the square button first, and then pushing the joystick forward. The leaping start helps during races.
When riding through obstacles like falling logs and giant snowballs, don't be afraid. Just keep going. But, this doesnt apply to all the areas. The rolling log 'valley' in Forest Trail 3 requires timing, but if you don't want to go back and get your horse, simply lead the foal all the way across it, tie it up, and then whistle for your horse by pressing the triangle button. You won't lose trust on the Friendship Meter if the horse gets hit by a log, which it won't. The game is very strange that way.
It seems that obstacles can hit you when you're with or without your horse, but when your horse is without you, it doesn't seem to get touched by obstacles like falling logs or wild animals.
I wouldn't try that with the bears or elephant seals, though.
When racing in the forest, yeah, always stick to the inside. Just keep the joystick pressed forward when you're on the stone wall and about to jump the gaps.
Teresa's already easy to beat, Christie's a little harder, but Mrs. What's-Her-Name takes careful planning. I still beat her on my first try, though.
I've been playing this game for a really long time. Even though I beat it a long while ago, I still like to take my favorite horse out on my favorite trail, Forest Trail 1. My fave horse is Blossom, though I've mentally renamed her Windwaker, after an imaginary horse I thought up.
I made her a palomino, and she's my fastest horse, at least, that's what I believe.
For you beginners out there, just go with the flow of the game. It gets really fun, and it's even challenging, so listen to the tips I've given you, and be sure to pick a good horse to be your racing one.
Mine's Blossom in my game, but I think they're different for everyone's games. Have fun!