I have no experience using a GPS in blowing snow and cold, but those factors roughly triple the difficulty of doing anything. I'll bet using a GPS would be very tricky....
I did have a little test run in pretty much as close as you can get to controlled circumstances when the weather turns bad above the three line: I've used my Magellan Meridian in a gale (beaufort force 7), somewhere between -5 to -10C, drifting snow and about 50 meters visibility. I have a custom made nylon GPS case that is clipped to my map case. The combined map case and GPS case is worn at my left side, with a strap over my right shoulder. This setup doesn't dangle or flap around. I can lift my GPS and push the buttons without removing my mittens. If I choose the menu with a big fat arrow on it I can check my course on the move - but anything more complicated than "a bit to the right/left" and I need to stop and think for a couple of seconds. When the wind blows that hard, thinking is actually quite hard. Communicating is even harder...
Having to stop every now and then is in itself dangerous. Your group may come apart very quickly, which is the big nr. 1 no-no. Frequent stops also cause irritation in others - they want to move, not stand still and start to freeze while you fiddle with your GPS thingy.
Even the best setup will fail when your googles start to ice. Hard to read the GPS when the googles are nothing but a greyish blur... I didn't experience that, but icing is just a matter of having the wrong set of circumstances. Again, a big fat arrow may just be visible through the blur. If not, you have to stop, turn your back to the wind and lift your googles to have a peek.
Traveling under such circumstances is doable, but requires training, discipline and alertness. Someone who doesn't pay attention for a few seconds may easily find that he has vandered off from the group while you fiddled with your GPS. Now your little trip has turned into a zero visibility search-and-rescue scenario.
The wise man will dig in and save the energy for better weather.