12:56 p.m. on May 2, 2006 (EDT)
Having spent a bit of time in storm situations on Denali and other peaks, I have to reinforce some of Tom and Dave's comments and add a few others.
First thing is to determine what you mean by "extreme conditions." I have spent a lot of time on mountains where wind speeds exceeded 50 knots, and some above 70 knots (these were measured with a pocket weather station, a Kestrel 4000, on several North American mountains, including Denali, plus measurements from a nearby weather installation the rangers on Denali had at 14,000 and 17,000 ft). I have also encountered winds in the 50 knot range during winter trips in lower 48 mountain ranges, including 60 knots according to the meter at the weather observatory on Mt Washington. This places a constraint on your wind generator that it has to be able to withstand winds of that level for sustained periods, while generating the required electric energy. In the Alaska Range and in winter in various of the western US mountains, plus the Presidentials, temperatures can frequently range doen to the -40 deg range. This places a temperature durability constraint (the gear must operate at such temperatures or even lower), plus the energy output must be sufficient if the windspeed is only a 5-10 knot breeze to still provide the needed heating.
If climbers are going to carry this unit, it must be extremely light weight and compact. Otherwise, it will just be too much weight to add to an already too-heavy pack. In addition, It must be easy and quick to set up, while still being durable enough to withstand the wind and temperature conditions.
As Tom noted, it may be necessary to store energy for later use. Electric energy storage devices are still rather low energy density, I suspect, whether the newest battery technologies or other energy storage approaches. Thus you may not be able to meet weight constraints in storing the energy and have to be content with real-time generation, which puts a major constraint on the minimum efficiency of conversion of wind to electric energy.
Here are several bits of data you need:
wind energy density as a function of wind speed and altitude
efficiency of conversion - (1) the wind machine itself (Darius machines are not particularly efficient, nor are some of the other vertical machines, although the Darius-type could conceivably fold up compactly); (2) efficiency of the generator itself (do you need a permanent magnet to "prime", or can you use a small battery to prime e-m coils?). Keep in mind that this is a function of wind speed - many present wind generators have maximum allowable wind speeds. (3) efficiency of conversion of electric energy to heat (this is a very weak spot for electric heating)
structural requirements - material strength of the generator assembly itself, including the rotor; bracing/guying to support the device in strong winds; anchoring (can you anchor in snow or ice, or loose rock rubble, or more solid rock - can't drill bolt holes during an emergency situation.
cost constraints - it will have to be cheap enough as well
Dave and Tom noted a couple ways to reduce the amount of electric energy needed - heat only the sleeping bag, or a thermal suit (the TNF one Dave mentioned, or something similar to NASA or military pilot electric longjohns). There are electric socks and gloves that run off C or AA cells, which could be used as a basis for figuring the conversion efficiency and output rates.
Melting snow or ice for water is a high demand. Remember that it takes 80 kcal/liter of water derived from ice, IF the ice is at 0C. Problem is that on high mountains that are already at low temperatures, the ice would have to be heated up to 0C, and you have a lot of loss to the surroundings, unless you put the ice in an insulated container, so that the heat does not escape as fast as you melt the ice. Then you need to heat the water to a usable temperature (you lose body heat when drinking water colder than body temperature, not a good thing in an emergency situation), at 1 kcal/deg C/liter.
Tough problem. But, hey, it's just an engineering problem. And what do I know? I'm just a scientist (theoretician, at that) who has wandered around the hills for a couple years. (sign above the work station of one of our top-notch technicians where I worked before retirement - "A scientist is an engineer who can't design anything. An engineer is a technician who can't build anything.")