Honestly my first mental picture was something more like a really low rate of fire Splatoon except more about knocking down enemy “fortresses” instead of just coating the other side since… it’s snow, it’s already on both sides.
Different weapons would be stuff like slings for range, or a shovel for busting down snow castles, maybe it has a charged up projectile where your character gets a whole shovel full of snow and then lops it overhead to try and nail someone with an air mailed avalanche.
Also have an actual gun sometimes show up on the map but if you grab it all your shots miss for like ten seconds because funni.