I've always been wondering why nobody tried the dummy batteries (EP-5B, EP-5C, ...) that come with external power sources.
Should be an easy nerdy task to build a battery pack that fits your pocket or the inside of a down jacket, with an appropriate extension cord and a connector to the dummy battery.
Little or no stress on the battery, I guess the freezing and thawing is not exactly good medicine for battery life.
My minimum with a digital camera has been -25°C for 3 hrs (no problem there), should operating time increase and temperature decrease in future outings, I certainly will be doing some experimenting with dummy batteries.
Ciao from Massimo