As you know, the north wall in any house is going to be the coldest. The streaks that you have on the wall are nothing more than dirt stains. The reason that they are there is because a drop in temperature will create more moisture on the wall, and allow more dirt and dust to cling to it. The dirt is showing up in streaks because they are following the 2×4 studs lying behind the drywall. The insulation between the drywall and the outside wall is placed in between the studs. The studs themselves are not insulated, and the wall in front of the studs are colder than the rest of the wall. What you have to do is insulate the studs. The easiest way to do that is to install rigid foam paneling over the studs. You can either tear down the existing drywall, install the paneling, and erect new drywall, or place a 2.5 cm (1 in.) sheet of rigid foam over the existing drywall and add a new drywall over that. This is the simplest way to correct the problem, however, you will have to make the electrical boxes and window frames flush with the new wall.