as a psudo guide
once it goes to about 32* F i am done with Ni-mhy, and alkaline.
once it gets below 0*F i would chose for the lithium and not li-ion.
above that from my test for myself and knowing that the light and discharging the battery has some heat occuring, i would still use the rechargable.
for me it would depend on How cold. and that is probably where i would draw the line.
i have had ni-mhy get "weak" acting at right below 40*f , which is barely even getting cold, i was like whats your problem little battery.
i have put Lithium and li-ion in the deep freeze Running at -13*f and they didnt even budge, came out with frost forming on them (which is another problem) and were going just as strong as when i put them in.
speaking of frost forming, condensation and all, a li-ions protection curcuit would not like to have water condensation occur in it.
like any electronics and cameras and all bring them in from the cold the water in the warmer air can condence on parts that hold the cold.
while a protection PCB cant "hold" a lot of cold , and there isnt a lot of air passing by it, it could get condensation on it when going from cold to the warm.
SO
not all cold problems are the chemicals getting to cold and slowing thier reactions down, be it a cell phone or other electronics, might be good to remember.
after getting into the warmer zone , the device will get back up to the room temperatures and all is well again.