Here are a couple of Panasonic NiMH cells intended for low temperature operation. I don't have any experience with them as I just discovered them online tonight.
BK250A : Low temperature discharge type (NiMH A Cell)
https://industrial.panasonic.com/ww...l-metal/Low_temperature_discharge_type/BK250A
BK130AA : Low temperature discharge type (NiMH AA-Cell)
https://industrial.panasonic.com/ww...-metal/Low_temperature_discharge_type/BK130AA
I recently purchased a 1200 lumen bicycle light with a battery pack with four 2,200 mAH Li-Ion cells in it. At 80 degrees F it will run for over 2 hours. However, at 20°F in will only run for 12 minutes. I'm not sure how much of the problem is the actually Li-Ion cells and how much is the undervoltage protection circuit tripping too early.
After looking at a lot of Li-Ion information I've come to the conclusion that at present Li-Ion cells aren't that suitable for winter use in Minnesota.
Check this out: Study on Low Temperature Performance of Li Ion Battery
https://www.scirp.org/Journal/PaperInformation.aspx?PaperID=80512
Look at figures # 4, 5, and 6. At higher current drains the internal resistance of the battery has become so high that there is nearly no output at -22°F (-30°C).
I think what it may indicate is that a Li-Ion cell with very low internal resistance (High current output / High drain) may perform better and provide more mAH of output than a lower drain Li-Ion cell with a higher mAH rating at higher temperatures.
I suspect that some of those high current Li-Ion cells designed for vaping devices might work better at lower temperatures. Alternately you may need to connect multiple Li-Ion cells in parallel to obtain sufficiently low internal impedance at low temperatures.
Until I obtain different batteries, I've put the Li-ION battery pack into one of the panniers on my bicycle stuffed full of insulation. It has extended the run time substantially in this subzero weather. The other option if to fashion a harness to hold the cells next to my body to keep them warm.
Previously, I was using a modified Stanley spotlight with a 540 lumen output on my bicycle. I gutted the electronics and ran the LED array directly from a 4 pack of NiMH AA cells in series using a power MOSFET to turn the power on and off. It actually performed fairly well in subzero weather, until it was stolen.
Scott Novak