No, you really don’t need a special pack as the chances are you’ll be able to wear your boots and helmet to make the (hopefully short!) trip from your accommodation or car to the slopes. We suggest that you might find a ‘bum bag’ useful for some small items like your smartphone, sunscreen, wallet, etc, and maybe even a water bottle.
Or, if you’re an experienced skier or boarder and are planning a more adventurous itinerary away from the well-managed slopes, then you’d be wise to look into buying a ski backpack like those recommended above to carry all the gear you’ll need.