You may have a problem called thermal bridging but we need to see inside the wall to fully understand it. When it gets cold outside, the insulation in the wall cavity does a good job of keeping out the cold, but the uninsulated wood framing allows a lot of heat to escape, as wood is not a very good insulator. All this heat loss through the studs means that the winter cold is moving in through the same path. Besides making the wall cold, moisture can collect on the coldest spots over the studs, and trap dust from the air-resulting in dirty stripes on the wall. If it gets cold enough to cause serious condensation, then mold can start to grow. You may not realize it but more than 20 percent of our walls consist of wood framing, not insulation. That is the equivalent of a hole in every home the size of a garage door that is left uninsulated. Putting rigid foam insulation over the wall, inside or out, will insulate the wood as well as the wall, blocking the heat loss. If you are residing in the house, insulate from the outside. Otherwise simply put rigid foam insulation over the wallpaper on the inside and put new drywall over it. A few adjustments to the window frame and electrical boxes and your north wall will be considerably warmer.