I think instrument choice is the most prominent "source of snowiness"

In particular the one that arrives starting at 0:12.
The chorus that you put around 0:50 too (people singing Christmas songs in chorus, "Joy to the world", etc

)
I agree that you could reduce the volume/amount of the percussions (but not change the beat), but I'm ok with the way it is now. It has to be at the same time rhythmic, because it's a high-speed race, but snowy...
Maybe you could introduce a theme, like you did with the one from TuxRacer, but from a Christmas song? Personally I love
Carol of the bells (used in Home Alone - very snowy and Christmasy film

).
EDIT: I'm listening to the song right now, and it's quite epic...maybe you could search in the "epic" direction for your song - just a thought
