I never been to such places but I think there's not much to be aprehensive about.Unlike film cameras where the only electrical circuit
is the meter with a coin battery the digital camera is all electronic.So when it's operating it generates heat on it's own because of circuit resistance,like the LCD screen,focus motor,stabalising motors and battery also gets hot.Just keep camera close to your body or you can use a thermal bag,those that keep drinks hot.10 degree celsius is not that extreme.Bear in mind that the commercial grade integrated circuits are speced at 0-70/80 degree celcius only even miltary ones are towards the higher temperatures.And the grease for the mechanicals that are used will not freeze up.
the only thing to worry is the reduced battery life in freezing cold environment, just bring 1 or 2 extra batteries (and keep them warm) and you will be fine, you should worry more about yourself, cameras are tougher than us.
I've had problems where it cant detect my Lexar cards when its cold. (dun ask me why) I had to use other cards for that trip whenever I shot outdoors. Indoors where it's warmer, I had no problems. So do bring a few more cards along.
My batteries also tends to die faster, always try to keep your camera under ur jacket or close to your body when not using it, and definitely bring spare batt.
Fogging can be a problem too when u go into a warm area suddenly. Try to keep your camera in your bag before going indoors, so that the bag itself will allow a more gradual increase in temperature and prevent fogging.
Remember that snow will melt, so do wipe the snow off your camera and increase exposure when shooting snow.
My 5D MKII amazed me when it functions normally even after dropped into snow, bombarded by snow, during dog sledding. And you know once your camera drop into snow, all possible concave areas will be filled with snow, and that includes the CF card area.
Actually, Gornegrat is lower in altitude, so it was at minus 9 deg C. We braved minus 15 deg C up at the top in the Glacier Paradise, at 3883 m / 12,740 ft, but only for 5-10 mins at most just to experience it [see here]. (At Jungfraujoch, "Top of Europe," it was minus 11 deg C.)
All three mountain tops had strong wind blowing, and snowing. Very nice, but only if you are adequately clothed for the cold, especially with good shoes that are waterproof and can keep the feet warm.
I carried the camera in a Canon Crumpler bag, which is padded and kept the camera relatively warm. Still, the camera got very cold when out for just a few minutes at that exposure; thankfully, it didn't freeze up or fail. The Lexar 32GB Class 10 SD card worked fine.