The following suggestions should be "exciting enough" to encourage some people's attention. I'd be pleased if people checked by R value and thermal store figures to ensure I hadn't missed a power of 10 or few - I think the figures are correct but will recheck when I get time.
You are somewhat below the lower border of what anyone seems to provide information on. The limit tends to be electrolyte freezing and the effects thereof.
SOME manufacturers specify marginal operation down to -20C but most say -10C.
-20F = (-20-32)*5/9 = -28.6 - say -30C.
I'd "guess" that cells which were well insulated and which had a degree of "thermal battery" included (see below) with no external heat source would have a reasonable chance of surviving -30C for say weeks at a time, [possibly with some damage].
However, it seems likely that a system able to maintain batteries 'somewhat above this' is achievable with a probably acceptable amount of effort and probably quite low expense.
Some batteries will be better than others (due at least to electrolyte issues) and if you have not yet made a battery choice then engaging with the manufacturers could be worthwhile.)
The suggested system could be trialed at pilot scale in a domestic freezer to provide the concepts and the figures.
One approach is to provide a well insulated wintering box and some 'clever tricks.
I'll assume your cells would fit in a 500mm a side cube.
That area = 6 x side^2 so here A = 6 x (0.5m)^2 = 1.5 m^2.
6 x (Internal area of a side) is close enough given that R will be only approximate
In practice the larger external side areas is offset by the increased path lengths at the edges and corners. If you REALLY care, make a sphere :-).
Scale as required.
Insulation material is rated in R value.
R = degree C x meter^2 per Watt
degrees F x feet^2 per BTU.
I assume those are equivalent (will check sometime :-).)
I'll work in real engineering units :-).
An R value of 10 means that per Watt the product of area insulated and temperature drop across the insulation = 10.
R = 10.9 for 3.6 inches (arcane units) of fibreglass "Batts"
R = 18.8 for 6" of fibreglass Batts.
Brick is about 1 R per inch.
A concrete block with voids filled has R~= 1.9
Fibreglass "Bats" seem liable to be what's wanted.
So an R value of say 20 should be doable with about 8" of bats around a 500mm sided cube.
8" ~= 200 mm so the 500mm a side cube crows to about 900 mm a side.
That's not tiny, but it will pack away under a tarp and a few branches from Spring to Fall and be available in Winter as needed.
SO if you can manage R=20.
Watts = degrees C drop x meters_squared / R
( W = C.A/R )
Here for 20 degrees of internal temperature above ambient
= 20C x 1.5 m^2 / 20 = 1.5 W
E&OE, but, apparently.
Double the sides to 1m and a total 6 m^2 and you need 9W - and a lot more insulation of about the same thickness.
Where to get the energy?
If you can manage solar thermal it could work well - I have seen evacuated tube heaters without water connections on a very chilly day with wisps of steam leaving the exit that was so hot it would badly burn a curiously offered finger - ask me how I know :-) :-(. A single close to vertically mounted single evacuated tube in good sunlight in say - 30C conditions could provide all the heating you need - see further below.
It deepends greatly on situation, but a solar panel that can keep
snow free (there's a trick) that gives 36 Wh/day - probably less needed on average, would suffice.
If you thermostatically switched the heaters in at say - 10C and kept Tinternal in the 0C - -10C range the mean consumption over months would be lower.
The environment may not be kind to wind turbines BUT a 1.5Watt average output wind turbine can be as rugged as all get out and quite small and a 10 Watt one not vastly larger.
Wind mechanical !!!
You COULD arrange mechanical friction heating (pole above cabin with shaft through roof - maybe down chimney. Mechanical thermal conversion efficiency approaches 100% after squeaking :-).
Battery Self heating:
If the really low temperatures occur seldom enough and the battery is large enough and you are keen enough with the R values then starting with a fully charged battery lightly topped by solar panel until the snows set in MAY allow the main battery to fend for itself. Thinks ....
A vv rough estimate suggests that if you stacked 18650 cells in a 20mm x 20mm x 100mm grid giving 25000 / m^3 and used a 500 mm ^3 store area = 1/8 m^3 and filled 80% of this = 2500 cells each about 10 Wh (conservative) you'd get 25 kWh in my example space. At 1.5W (lets say 2W) that's 12500 hours or about 18 months.
Allowing for much reduced battery capacity and a useful Vmin safety margin a battery pack alone with R20 heating should easily self maintain above crucial temperatures.
Then there is phase change storage. Water freezes at 0C and saturated saline solution at about -18C (which conveniently, is -22F. A saline solution can be designed for any freezing point in the -18C - 0C range.
Correction - watt hours wastoo high by factor of 10 :-(.
Latent heat of fusion of water is about 334 Joule/CC.
That's 334,000 Joules per litre - or about 93 Watt hours of thermal storage per litre. So IF you could keep your battery above say -10C with 1.5 Watts then 1 litre of water will provide protection against -30C (-10 - 20) ambient temperatures 24/7 for about 4 days. When the temperature drops to the freezing point the water starts to freeze and as long as you can maintain good thermal contact with water and air then the temperature will not fall below the freezing point until all the water is frozen.
If you can input energy from an external source any time it is available it can add to the thawing and store the energy.
If you have say 1 litre of water that freezes at 0C, another set at -5C another at -10C .... you can have a graded thermal battery.
My original 500 mm cube has 5^3 = 125 litre capacity, so even a say "massive" 10 litre "thermal battery" will only occupy 10/125 = 8% of the storage capacity and give you about 40 days of protection when temperatures are below -10 or -20 or ... degrees C.
This is getting "a bit fancy but could even be doable.
Imagine a system with an "icetank" inside the insulated volume, with the iceblock being able to be dumped via a trapdoor. During sub-fluid-freezing conditions the water in the insulated chamber cools, thereby clamping the chamber temperature at t_fluid_freezing. However when ambient temperature rises above fluid freezing the ice clamps the chamber at the same temperature. This is not totally terrible but it would be good if the ice did not clamp the chamber temperature when heat was available. IF the ice could be dumped, new liquid could be introduced from an external tank that is better able to thaw. Fluid from a slowly melting external tank could be allowed to drain into the chamber. While this is beginning to sound somewhat "Heath Robinson" it would be relatively easy to implement.
Even just providing a head of warmed fluid on an entry tube to an internal tank or internal external circulation would allow a similar result with perhaps little more than a thermo-syphon or very low power occasionally operating pump.
REAL WORLD EXPERIENCE.
NO measurements - but this worked for me.
Well wrapped "dry ice" placed in a normal insulating "chilly bin" with water ice slabs above it has a survival life of "a few days".
Build a insulation prison with a LARGE polystyrene chilly bin with domestic foam under floor insulation layers under it, a central cube space with the dry ice in it and more foam layers above so that the dry ice self cools in the approximate center of a foam block and I can achieve somewhere over a week with "some dry ice left"
Less than I'd like.
Enough for "Guy Fawkes" :-)