Open it up! If you don't have any vents, put some in. If you have windows, get them opened. If you can open the door, open that too! Then take out the wet shavings and replace with dry, because they'll stay wet underneath the top surface for much longer than you think.
We always think we are doing our birds a great service by buttoning our coops up tight against the cold like we would our homes. But it's not only unnecessary, it can be downright dangerous. As you've found, humidity builds up quickly, and that humidity comes from their breathing, their poop, waterers in the coop, and the weather conditions outside. Think of getting into your car on a cold day. What happens? The windows fog. Same principle. Humidity in a closed up chicken coop presents the added problem of an ammonia build up. Good luck!