Working in cold weather presents problems for both photographers and their equipment. Though some photographers used to more tropical climates might think freezing (32 degrees F or 0 degrees C) is cold, neither the photographer or their gear should really experience any problems at that temperature. Just about all cameras, lenses and batteries are rated for use down to freezing (32 degrees F, 0 degrees C). However at lower temperatures there are a few things that may cause problems.
..Though most digital cameras are specified by their manufacturer only for operation down to a temperature of 0 degrees C (32 degrees F), most will work perfectly well at much lower temperatures. They aren't rated for lower temperature work because they aren't tested to fully meet all specifications at those temperatures and because there are some problems that can occur as detailed below 0 degrees C but most of those problems can be avoided. Electronics actually often work better at lower temperatures, so there's really no issue with the electronic circuitry.
The problems which may arise in very cold weather are usually either mechanical, related to LCD displays or related to battery issues. At just what temperature problems occur depends on the exact design of the equipment, but most modern cameras and lenses are just fine at -20 degrees C and can even be used down to -40 degrees C with a little care and attention....