Idea 1: 2D Platformer where you have a limited time to finish the level before you freeze to death.
Idea 2: 2D Platformer where you have 3 lives to finish each level, there is a 10 second timer before you turn into an ice cube, after you die the ice cube will stay for your next life. The Idea is to die on a button that opens a door so that next life you can finish the level by going through the door.