The cold thickens lubricants in the camera and seriously shortens how many shots you can get from a charged battery until the battery is warmed up again.
Another issue with cold temperatures is cold air holds less moisture.
Relative humidity, the % of humidity in weather forecasts, is a function of temperature.
100% humidity at 100°F has a lot more moisture in the air than 100% humidity at 20°F.
Very low absolute humidity is hard on shutter curtains and seals. Cold air at 100% humidity has a lower absolute humidity than warm air.
Dew point is another factor.
Relative humidity of 100% indicates the dew point is equal to the current temperature and that the air is maximally saturated with water.