In reply to Aigen:
I've stayed in several Austrian, Swiss, French & Spanish 'winter rooms (often the whole hut) & have always found them open, although, as you say, a shovel is often needed to clear the door. That said, always worth checking the hut will be open & most have websites or other contact details.
Are you looking for a large hut or somewhere small ? I once spent a night in the Schoenbiel where the entire hut was open but it seemed a bit creepy with only 2 of us, the following night in the Cabane de Col Brulée (small bivy hut) was more pleasant.