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.