I've had my D200 out in -20F weather, but not for days at a time (we're talking maybe 4-5 hours at most) without damage. As mentioned, the first thing to die fast is the batteries. When cold, power is lost fast.
Under those conditions, I do not use the battery grip, but have 1-2 batteries in a shirt pocket close to my warm skin and 1 in the camera, and swap them out about once every 30-60 minutes for best functionality.
Keep a microfibre cloth handy and make sure you *DO* have a protective filter on your lens, as you will be wiping it pretty often when snow gets on it. I saw a guy with a clear showercap over his camera on the slopes once. He had cut a small hole in it for the lens and wrapped the rest of the camera in a protective plastic cover. I thought that was rather clever of him.
My D200 is weather sealed, but this could be a good idea for you to consider if you get the camera covered in snow and wet often during a day skiing.