You better worry about your ventilation. That a heckova lot more important than worrying about them getting chilly. From what you posted, it sounds like you sealed off the fresh air/ventilation. You might want to give serious thought to opening it back up. Moisture won't just go into your coop, the birds themselves WILL generate it. And if it is not properly ventilated out, you WILL have problems.The ventilation is not what I am so worried about. However any mishaps that may happen with water in the coop such as, spills and leaks, not taken care of quickly in temperatures like this could give them frost bite or worse kill your flock. In the summer mold could happen with spills or leaks, so I just avoid having water in the coop.
-Frozen Wings
I have an open air coop. Water has always been kept inside year round. In the summer, rain has blown into my coop. I've never had any mold problems, because my coop is well ventilated and drys out quick. Fresh air flow is the answer. You have that and you don't ever have to worry about mold.