Reboot phone due to cold weather

I am not familiar with iPhone batteries but most batteries will recover to a good degree after warming again. In your case it sounds like the cold may have weakened the battery power to the extent that the low level caused the electronics to not work properly and the device, uh, crashed. Let it warm up again and see if you can reset it.

Keeping iPhone, iPad, and iPod touch within acceptable operating temperatures - https://support.apple.com/HT201678

Hello b_keefer,

If your iPhone, iPad, or iPod touch won‘t turn on or is frozen, click here --> https://support.apple.com/HT201412 - Read it all, including the final step to Contact Apple Support if necessary

I don't think it means literally frozen but you get the idea...