The click you describe may be coming from the starter relay. If your battery is low then it won't have enough power to turn the engine, hence click and nothing. Check the voltage on the battery - should be 12.5 or better and 13 plus when the engine is running. If the battery is more than five years old this cold weather has probably killed it. If it's newer check the alternator drive belt is properly tensioned and the alternator is charging properly.
Richard
December 2008