That's one of the problems with those small, prefab coops. :(
The northerners can provide more details, but chickens can tolerate a lot of cold if it's dry and draft-free -- they've got built-in down parkas. But the moisture from their breath and their poop has to be able to escape or it...
Hopefully some northern chicken keepers will chime in, but my first thought is to suggest a louvered gable vent to let air flow without letting rain/snow in.
Plenty of ventilation will be your best friend here. You'll want to aim for 1 square foot of ventilation per adult, standard-sized hen.
My test to know if I need more ventilation is to put my head and shoulders into the coop on a warm, sunny day. If it's warmer in than out I need more...