You'd probably get away with it if you used materials like straw instead of plastic, and so long as none of the plant material or the pots is so close to the glass as to get dripped on. The worry is whether it drips down from the glass ceiling and if it does, how much of it there is. It must be a lot warmer inside than out, or you wouldn't get the condensation forming... Probably sensible to get yourself some sulphur dust and use it on plants in there to help prevent fungal infection.

I would leave the door open as well, just closing it when the temperture is forcast to get below zero.

Even when it is raining you need to keep the air circulating so door and or window open unless temp. is likely to drop below zero.

Have you thought about installing one of those self opening windows in the roof? They contain a wax cylinder that expands when the temperature rises and causes the window to open. You can adjust them to open at the round about the temperature you decide on.