What type of battery copes best with low temperature?

LiFePO4 - Lithium Ferro Phosphate - chemistry is often rated to -20C and in a large minority of cases to lower.

Voltage per cell is on the low side of Lithium Ion - 3.6V max on charge and typically 3.2V on moderate or low load and 3.1V on heavy load.

Custom external battery pack:

Making a custom battery pack that connects externally is probably worth looking at. If I was in your situation I'd consider making an "octopus of cables that can use a central battery pack to operate several target devices. This would allow you to locate the battery pack somewhere optimal - perhaps rear belt or small of back mounting to use body temperature.

Obviously cable connection reduces mobility and flexibility and may not be acceptable. At one stage I needed very high camera battery capacity over many hours. I made a lead acid based supply operating from a 6V 7AH SLA flat battery. This arrangement had the same capacity as about 4 x 1.4Ah x 7.2V Lithium Ion camera batteries and a good current capacity.

I ran a power cable from the camera up the strap, fastened in place as required to provide flexibility while not risking being snagged. That much of the arrangement was functionally the same as a standard camera as cable was not evident. I provided a cord from the top of the strap down to the rear belt battery pack. This was a suit coat type shooting environment and the cord could run down my back under the coat.

Lead acid is substantially heavier per capacity than LiIon. This was entirely acceptable in my case, but an off the shelf LiFePO4 would do this job well as long as Voltage needs were met.

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The link below is broken as the organisation changed websites. May be fixable. In lieu, thiis is useful -Lithium Ferro Phosphate Batteries

Dead -Good LiFePO4 overview - notes -20C temperature limit.

A123 claim operation to -30 C.

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