Sure, but there are insulation solutions that mostly prevent it. For example insulation foam layered between vapor permeable foil on the cold side and vapor inhibiting foil on the warm side.
But drywall (and other porous surfaces) are supposed to help regulate moisture, so if they never get an opportunity to dry because it's permanently cold and humid, yeah, that'll be a problem. Cracking a window at least 30 minutes per day (ideally on dry days) does wonders, though it won't help temperatures in winter.
Yep in theory it's all nice and easy, just put foils in and open the windows sometimes.
In practice... say, there is a dog that likes to gnaw on corners and thus punctures the vapor barrier. Happened to my own house's outside insulation. That's just one of many "unforeseen" ways how these foils and barriers stop working. I fully expect the polystyrene there to get moldy in 20 years or even less.
But drywall (and other porous surfaces) are supposed to help regulate moisture, so if they never get an opportunity to dry because it's permanently cold and humid, yeah, that'll be a problem. Cracking a window at least 30 minutes per day (ideally on dry days) does wonders, though it won't help temperatures in winter.