I am remodeling a 1924 bathroom in Minnesota. The current cabinet is a wall-hung 1960s beauty. Wife would like a classic style inset cabinet. I have taken down the lath+plaster, so it would be easy to frame it in. Obviously, there will be no insulation behind the cabinet--just the exterior sheathing. Is the stuff in the cabinet going to freeze? Should I just try to do a mirror or something like that?