My car makes a rapid clicking when I try to start it. Car won't start below freezing temps. Is it just bad battery? See description?

Update: Rapid clicking (lower pitch), Gatling gun continues as long as key is turned. Everything electric in car works 100%. I've left it on for 10 min just to see if the electric to the car would "die". It did not. Shouldn't the lights dim or electrical stuff in vehicle have problems too. I jumped it... show more Rapid clicking (lower pitch), Gatling gun continues as long as key is turned. Everything electric in car works 100%. I've left it on for 10 min just to see if the electric to the car would "die". It did not. Shouldn't the lights dim or electrical stuff in vehicle have problems too. I jumped it drove 4-5 miles and it worked for about 1 day. This just happened. It happened second day of below freezing temps. Making dead battery soundelectric in vehicle is fine. Anything else you can think of?
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