Not sure about the cold but you can significantly improve battery life when walking if you select airplane mode. Your phone without a wifi, Bluetooth or mobile phone signal is constantly hunting for them, and GPS also drains the battery.
I was thinking about stuff like that as i had a soak in the bath just now.
Given that I don't use phone to navigate (like you I prefer GPS as main nav tool, but maybe unlike you I use map and compass as the back up...if I altered that...would probably just get a second GPS as back-up option.)
I could just shut down phone completely at start of walk, then only "power up" when I specifically want to send a message/ picture or whatever to a friend.
Stupidly...I've been leaving phone on in normal mode up to now, although 99% of time I do nothing with it!
I think your suggestion of just leaving in airplane mode has slight advantages to my idea of complete turn-off...faster to get back in normal again by just de-selecting airplane mode to use phone for a short while, rather having to completely re-start from complete shut down.
Thanks