My car has started squealing--fan belt?

It is most likely the alternator belt is loose. The cold probably is related to the problem but I don't have a good answer to the reasoning behind it. Could it be that the alternator needs to work harder to charge the battery in the cold weather? The belts do stretch so it might be a simple adjustment. But with the cold weather you should have the belt examined for wear. It could be at the end of its life cycle and you don't want to be caught in the cold with a broken belt. If a belt slips too much it won't charge the battery and you could be caught at night without enough power to light the headlights.