iPhone 4S cold weather

Hey, I was wondering if aNybodies phone turns itself of it cold weather.

My phone can be fully charged however when I am out in cold weather it will turn itself and say the battery is dead. I have to get the phone warm again eg. rub it or go inside for it to turn on again and still be fully charged.

If I am outside when it turns back on it only usually lasts around 5-10 mins before it turns itself back off. Also my battery life does not seem to last long in cold weathers.

Does anybody know of apple would be able yo do anything to fix this ridiculous phone/issue I'm having?