Your problem is potentially two fold, primary is lack of insulation combined with lack sufficient air flow to keep the interior wall surface from frosting in extreme cold. this is the first.
When the interior warms up enough this frost turns to damp, cycle this enough times and it turns to mold.
The second probable cause is inadequate vapour barrier. Fiberglass insulation rapidly loses it insulation value if interior vapour can penitrate it.
If poorly installed and or no vapour barrier is present, installing exterior insulation, usually foam, will rot your house from the inside out as it is a vapour barrier itself and is on the wrong side of the heating surface in this case, will trap moisture within the wall cavity.
Myself, I would take one of your smaller rooms that has an outside wall and rip off the interior surface of it, drywall? Then you will know what you are dealing with.
