Wow. I have never seen that error and it rgularly gets colder than that here in the winter (although not this winter so far). Sometimes I am outside for 40_ minutes at a time too. Perhaps the core of the phone wasn;t able to cool down to that point.
I live in Canada and have never had any issues with my phone not working in the cold. It was -24C yesterday and I had my phone out with me. When its that cold though I'm not outside for long (usually just running between my car and buildings). I also keep my iPhone in my inside jacket pocket so its pretty warm from my body heat already.
Wow. Kinda weird that this thread comes up today, as I kinda made the mistake of bringing my phone with me on my morning walk like I do every day. However, today was COLD!!! Only 11 F. I use the GPS with a walking app to chart my walks every morning, and just carried it with me today as I do every day. When I got home (after 72 minutes and some seconds), the phone turned on for a moment, then shut down. After not going back on 10 minutes later, I did a hard reset. The apple logo came up, then it shut down again, but only after looking like the battery had completely discharged (empty battery with only a thin red line). I put it on the charger, and then it acted like normal. It showed the actual charge at the moment (65%), and has been working normally since. So, that's my experience, and I will make sure not to repeat it. I had been out before when it was cold, but this is the first time the temp was below 30F. Nice mild winter so far here in NJ.
Got to -14.1C when it went asleep, I woke it, and played another movie - it's working just fine. The LCD is getting a *tiny bit* sluggish, it's hardly perceptible compared to other displays I've see in the cold. That said, works just fine.
First, thank you for your willingness to experiment!
So you kept it going the whole time? If so, that would keep it warmer and prevent the LCD from starting to freeze as well.