Small batteries for use in cold (but not freezing) environments?

I would suggest a lithium CR2032 battery. feel free to pick a large package or place a few in parallel.

Lithium Polymer will have lower capacity at lower temperatures.

However, to quote battery university,

"Lithium-ion works within the discharge temperature limits of -20°C to 60°C (-4°F to 140°F)."

As a side note, they often list 1mA as maximum current on one of these, but they can handle 10mA without much of a battery life loss(this will be worse at lower temps), pass 10mA and you will be killing batteries right and left.

Here is an example of a discharge curve based on temperature. It is the second page of the data-sheet. There is a clear decrease in life(~25%), but you should still be very able to use the battery. It looks like -20 degrees C is where you start to have large reductions.

Please let me know if there is anything I can add to make this more clear or more valuable to you.

I would not recommend the lithium batteries for low temperature applications. They suffer badly from low temperature, more than either the alkaline or NiMH chemistries.

I'd recommend Nickel-Cadmium (Ni-Cad) batteries, as they have have the best temperature range of any of the typical batteries, They also have very low internal resistance (less than half that of a NiMH) and therefore have very good maximum currents (think of an electric drill).

Some things to watch out for are their memory characteristic (Don't recharge it before it's almost dead, or you'll lose the capacity you don't use) and the fact that they contain toxic cadmium. Use a decent charger or charge IC, and you'll be fine. You might have some trouble trying to do a dT(emp)/dt(ime) cuttoff, and they don't have a great -dV/dt characteristic either.

Another idea (if you own the fridge) - Can you just open up the temperature control panel and light at the back of the fridge, get at the power source, say, for the light (before the switch, if you want it to be running when you close the fridge), and stick in an outlet or a couple (INSULATED! WELL INSULATED!) spade terminals and plug in a wall wart? That's what I'd do, rather than messing with batteries.