It's so cold that my iPhone battery, which was close to full, reported to the software that it was empty and caused the device to shut down.
I don't know how old your iPhone is, but it may just be a symptom of a failing battery. That's what happened to me 2 weeks ago. After my battery kept doing that in cold weather, I checked the battery health and it was indeed pretty degraded. I used this app to check the battery health: http://www.coconut-flavour.com/coconutbattery/
Thanks for the tip Dan. Here's a screen shot. The phone is pretty new. It's an iPhone 6s Plus, I got it about a month after they came out, sometime during the summer I think.
