Why is the interior wall cold to touch during the winter?
It could be just air leaks and simply caulking the exterior may remedy the cold areas completely. In addition to caulking, cold spots are typically due to the lack of insulation or a poor installation of insulation.

If caulking can't be put anywhere apparent or does little to nothing, then you'll have to rip the walls and corners open to air seal and insulate with the proper materials and methods.

There can't be any openings, gaps or loose fitting of insulation nor its seams and everything heading to the outside must be caulked.