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Inside pocket, where I keep mine, never went dead. But I’m not taking out and talking or texting all the time either, I’m there to fish
If it is a recent iPhone, Apple makes some decent battery cases that you could use to recharge it after using it on the cold sled. They can be a bit pricey though. Otherwise, I'd try getting a reputable powerbank from Amazon that you can confirm will provide the current/voltage appropriate for your phone. We have had good luck with the Anker brand of powerbanks.
Hand warmer attached to the back of the phone?