Would it be possible to use the shell of a dead battery to make an adapter, linked by heavy wire to a fresh and warm battery in an inside pocket? For my SLR system there used to be a chunky lead that filled the button-cell compartment with a plug and had four cells in a box on the end of a wire. It would be more tricky if there are hinged battery-compartment doors in the way of course.
Minus 4 centigrade isn't even very cold though, so the batteries could well be 'tired' as well. Did they work alright in the Summer?