This question really comes down to what, if anything, in winter sport scenes will be polarized, and then eliminating some polarity will make the shot better?
The first obvious answer is the sky if it's clear blue. The deep blue is not polarized, but the whiter haze in front of that is, depending on angle to the sun. By adjusting the polarizer to minimize the haze, you make the sky appear deeper and darker blue. Most of the time I think that makes for a better picture, but that is subjective and up to you and what you want to show.
Reflections off of ice at certain angles will also be polarized. A polarizer can be used to either reduce or accentuate these reflections. Again, whether that's good or bad and which way is up to you and what you are trying to show.
The diffuse white light from snow will have some polarization at certain angles from the sun. This won't be as dramatic as reflections off of ice, but could sometimes be used to advantage to allow the texture of the snow to be seen better and making it appear less blown out.
So yes, a polarizer can be useful for some types of shots in some conditions. Whether that matters or whether that produces a desirable effect is only something you can answer.
Overall, when shooting with snow around, be careful not to overexpose it. You might want to set the automatic exposure to -1 or so, or set it to take many points into account, not just the center. All the snow blown out is a lot more crappy looking than the little bit a polarizer will add back - unless of course that's what you are trying to do for some reason.