iPhone 5 cold shut down / crash

I've been skiing with my iPhone 5 for the last few weeks, and have had a problem with the iPhone shutting down in cold conditions. If the ambient temperature is below about freezing, the iPhone 5 will go from about 50-60% battery indication to shutting down and showing the "dead battery" logo when you try and turn it back on. If I warm it up in an inner pocket it will restart and show 50% battery again. I generally keep my iPhone in an outer chest pocket designed for cell phones on my ski jacket. I've moved the phone to an inner pocket and problem goes away. But that causes problems with getting to the phone for calls/etc, and also is an issue in terms of moisture. I skied for years with prior iPhone models including the iPhone 1-4 models, and never had this problem. I suspect it is something to do with the mostly metal case. I've done a full software restore and didn't change this. I'm planning to take it to the Apple Store next time I'm near one and see what they say.