The problem is not the battery and the cold. The problem is the silicone slug that acts as the button.
The switch on this light is a standard small push switch which is connected to the circuit board. The chunk of silicone that you push with your finger is about a half inch long and presses the switch.
The problem is that when this silicone rubber slug button thing freezes it expands and presses the switch, and does not let off until it thaws.
I am 100% sure of this. When I have the problem I can grab the button with my fingernails and pull the button away from the switch. Of course, this means removing two pairs of gloves.
I think that I am going to shave a small amount of material from the bottom of the button.