Sadly, eBikes tend to suffer from the cold.
Beyond the universal thickening of lubrication, stiff bearings etc.
Cold seems to decrease both, the output rate of the battery and the batteries capacity.
This malady seems to be fairly universal.
Best known are lead acid batteries on frosty mornings ... the grumbling of the motor trying to turn over, followed by the dreaded """click click click!"
SLA are noticeably affected, as are Nimh, Ni-cd, Li-ion, LiFePO4 and ... ?
Even alkalines ... flashlights seem dimmer when cold.
Output is reduced due to the cold increasing electrical resistance of certain components.
Increased IR (Internal Resistance).
Of course, cold does thicken all lubrication, causing pedals, crank, chain, freewheel, hub, motor ... everything ... to require more power to operate.
I've noticed,specifically with Li-ion cells, that the cold hinders the free flow of electrons.
Heavy throttle use demonstrates as a deeper sag in pack voltage, which provides restricted performance and prematurely indicates a low battery condition-warning.
While it might be difficult-inconvenient to warm and keep warm your entire bicycle, most battery packs are removable and can be stored in warm location till used. Additionally, it is recommended to add insulation around cells. A base of polystyrene foam and surrounding with closed cell foam, fiberglass, any insulation, helps.
Ideal are soft sided coolers, lunch bags etc.
They come in a great variety of sizes and qualities.
I took a 6 pack cooler and added a base of non-compressible polystyrene, topped with a 7/16" layer of waferboard ... for rigidity and protection.
I store my pack inside, next to a heater vent, keeps it nice and warm 80ish F.
While batteries should not be charged while overly-warmish, they do, discharge, perform much better at warmer temperature - not HOT! - 80 towards 100F.
I did consider the option of a pack heater.
After considering need and functionability ... I decided that I, personally, did not want to spend extended lengths of time in the cold, so prolonged battery exposure would be unlikely or seldom.
For those interested, I did find and research small, sheet type, heating elements.
While 12V rated, they could be run from 24-36V+ by running in series.
I will try to find my research and post it up.