Olympus has 4 models that are pretty resistant to cold weather. The Mju 1030SW and Mju 850SW can withstand up to -14 degrees Celsius while the Mju 770SW and 790SW can handle cold weather conditions as low as -10 degrees Celsius. These 4 shooters are also shockproof and waterproof. For the 1030SW, it is also crushproof up to 100kg load.

In cold weather, the rechargeable battery tends to drain faster. So whenever possible, keep the camera close to your body to keep the battery warm for a longer shooting time.