In the snowboarding minigame, the goal is to get from the top to the bottom of one of three courses while collecting balloons and avoiding obstacles.
If you manage to get a "great" ranking (over 70 points) on one of the coures you will unlock a new course (The 3 courses being Beginner (A), Expert (B) and Crazy(C)).
Your points are effected by the following:
Snowbarding can be very helpful for raking up the GP in the gold saucer, then again the GP award from it can be unpredictable so you'd be safer going with something like the submarine game or possibly Chocobo Racing.