I think it would be cool if there were an ice-box in game. It would need to be filled with ice of course. The main difficulty would probably be implementing the ice.
These might be prohibitively difficult, but I can think of a few ways to get ice during the winter:
1) Foraging. Ice would appear in your inventory just like a stone or twigs.
2) Leaving water outside, e.g. in a pot.
3) Cutting ice from a body of water. Maybe right-clicking a lake or river with a saw or an axe in your inventory.
Ice could be used to fill an ice box. With enough ice, players might be able to store food year-round. Ice might also be used to reduce pain from certain injuries.