Have been skiing in contacts for about 15 years and only had a problem once. My tip is take spares on the slopes as i once managed to loose a left contact and felt very sick by the time i got back to my hotel.
If your going to wear sunglasses buy proper skiing ones with foam pads around the back. Normal sunglasses arnt good enough you still get allot of light around the edges and can still get snow blindness. Its not nice trust me.