I know that a lot of brilliant engineering has gone into developing the space technology that we have. So, what engineering lessons about dealing with extreme cold and portable power sources do you think we can take from space exploration and apply to an Antarctic context?
(disclaimer: I am not a cold-environments engineer, but I work around them)
There's not as much scope for transfer as might initially be assumed. Let's look at @ventsyv's comments in more detail.
A recent study looked at power options for remote sites in Antarctica (ie, those only visited occasionally by people, and which may go one or two years without maintenance). They concluded that solar is great when it works, but is only useful for around a third of the year. Remember that the worst a solar-powered space probe usually has to contend with is brief eclipses, or, in the case of a lander, several-hour nighttime shutdowns. By comparison, an Antarctic site will suffer a blackout period which might be several months long, with very long night cycles and twilight periods on either side. The closest analogy here is a long-duration Mars lander; however, Spirit/Opportunity had trouble enough with winter daylight at equatorial locations, and Mars Polar Lander/Phoenix were not intended to survive the winter at all.
RTGs are in theory a solution to this problem, but are no longer used in Antarctica. The Americans deployed them as early as the 1960s for remote weather stations, but removed the last ones in the 1990s. The Soviets used them widely, and the last four were recovered only a couple of years ago. Leaving aside the questions of cost and security (unattended radiological materials are very, very unpopular these days!), there's also something of an open question about the regulatory context. The Antarctic Treaty does not prohibit RTGs (or indeed nuclear power in general - the US used to operate a 'real' reactor at McMurdo), but it does require fairly thorough environmental impact studies and prohibit leaving any nuclear waste. I can imagine that unless you have a very clear plan for removing the RTG after use, you would have problems getting its deployment approved.
Outside of the space environment, there is more flexibility for alternative power sources; the study mentions conventional diesel generators and propane thermo-electric generators, neither of which would be practical without an oxygen atmosphere. Wind turbines can also be used; again, you need an atmosphere of some kind for these! The AGO stations use solar power supplemented by wind during the winter, with a two-day battery in case of calm weather, and the operators simply accept the fact that the system will shut down sometimes due to prolonged unfavourable weather conditions. But it'll probably come back online. If the whole thing fails to start up again, which is unlikely but possible, you can say "oh well" and fly someone in to start it back up in the summer. This is of course completely impractical for spacecraft - both the restart and the tolerant approach to downtime - but it simplifies the engineering requirements immensely.
For smaller "place and forget" devices, with minimal power requirements, it is simplest to just use conventional batteries. These probes, for example, have eight D-cell batteries with a two-year lifespan - they may even be acquired off the shelf - and as the unit is expected to be buried by snow before then, two years is seen as fine. Alternatively, if the units are accessible, a two- or three-year lifespan for a remote installation would make it quite practical to schedule a battery change as needed. Most batteries are good down to around -40C, which would rule out very deep-field operations (which might be -70C) but is reasonable for coastal work. Likewise, electronics good to -40C can be obtained more or less off the shelf, or rebuilt with fairly simple equipment. This highlights that specialist batteries and electronics are not necessarily needed. The AGO paper notes that "industrial" grade electrical equipment is usually fine to -40C, might cope with worse, and can happily be left unattended at much lower temperatures if turned off and gradually cooled.
Interestingly, though, the disposable probes highlight an unexpected bit of technology transfer - the parachute used was the same type used for Viking!
I don't think there is much overlap at all.
There are 2 types of power system used for space exploration - solar and RTGs.
Solar panels will not fare well in the Antarctic where clouds and whiteouts are common.
RTGs produce relatively little power and are expensive thus not practical for terrestrial applications.
The environments are too different for any sort of direct parallels.