Fermentation Chamber Question

I constructed a ferm chamber using a mini-fridge and constructed a box to expand the size. I have am fermenting my first lager. Unfortunately frost / ice is building up on the perimeter of the freezer portion of the mini-fridge. The frost has started to encapsulate the airlock and the air lock water has become frozen. Two questions:

1. Any ideas on how to prevent the frost / ice build up?
2. Assuming the bucket lid is air tight and if the air lock water is frozen how would air escape the bucket?

Tonight I intend on getting a specific gravity reading to see if there has been any change since I racked the beer to the secondary so that should give me an indication of any activity.

1. Add a fan to move the air around inside the chamber
2. Use vodka instead of water

have a looksie at this thread, good info.

https://www.homebrewtalk.com/f51/my-mini-fridge-fermentation-chamber-build-256068/