Any water vapour within the box would condense when the temperature drops past the dew point. You said the box isn't completely sealed, so it's entirely possible that moisture will get in. Are the PCBs suitably protected from moisture, e.g. conformal coating? This is just a suggestion to rule out though, not saying this is the problem.
I was able to reproduce the problem reliably by bringing the thing cold indoors for a minute, to let moisture condense, then getting it back outside.
It freezes, things stop working.
Nothing actually breaks, the radio just gets detuned.
First time it broke after an hour, i closed it indoors, so all the humid air condensed inside.
Second time it still works, i closed it outdoors after an hour sitting there open.
As far as i understand it, the box, not being airtight, would accumulate moisture inside of it with variations in pressure, temperature and humidity - easier to get in than out.
So, after some time it would start to condense and freeze.
If so, would a coating of polyurethane help?
Or perhaps putting some silicagel desiccator into the box?
That module looks like some junk with a blob on the pcb. It might be that some bonding wire from that IC to the pcb became loose.
RFM12B, not the best, but i haven't heard much bad about it either.
Datasheet says it's rated to -40.
The battery at its voltage is one of the things that you must check as already pointed out.
It's one of the parametres being read out, and it's stable.
Is the current consumption constant or do you have some periodic, rapid increase of current draw?
Near-zero for most time, about 17mA bursts (1/4s) every 5 to 10 seconds.
Your capacitors could also be freezing, as they might only be rated for -10c to 70C operation. You probably have issues as well with the battery getting cold.
Aluminium polymer capacitors, rated down to -55*C with 1.25 Z ratio to +20. Should be good enough, i guess?
One solution would be to insulate the electronics and battery very well with polystyrene shehting so that the heat they generate in use keeps them above freezing.
Less than a milliwatt average?
Don't think that would do much.