You have to get to the bottom of the slope in 2:00. An ordinary run is about 1:50. So that gives you about 10 seconds of extra time to dodge those snowmen.
Your primary objective is to dodge those snowmen. Missing a gate isn't too bad as you have to miss five of them to get disqualified. A good tip is to go in first-person view (by pressing B). That way, you won't have a body blocking your view of the incoming snowmen.
Otherwise, try not to lose too much speed, hold RT the whole course, and you should get it eventually.