If you're able to invest in better windows (good double or even triple glazing), that will solve it. But just wiping down the window sill semi-regularly works well, even if it's an annoying chore.
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.
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.