Actually, processors are absolutely fine running at even -5C (and plenty professional water coolers try to get that low) with absolutely no performance hit and unless you go to bellow -15C, you won't encounter any issues besides a 3-4% performance drop. HOWEVER, the air needs to be cold, NOT cold because of humidity! Humid air will go inside the system and while it will cool it down, it will also leave part of the humidity inside, so after running a while it can ruin components.