The camera will probably be fine...as long as we are not talking about extremely cold temps...like -30 ~ -40 etc. Remember that the L in LCD stands for liquid...so you don't want your LCD screen to freeze. Lubrication on moving parts can also get thick.
The biggest functional issue will be the batteries. They loose power very quickly when it's cold. They get better when they warm up, so you can 're-heat' them to get some power back. It's recommended that you have at least two or three batteries and keep the spares in your pockets, under your jacket. Then you can swap them when the one in the camera dies.
Lastly, you need to be aware of condensation. When your camera & lens are cold and you take it into a warm & humid...condensation will form all all surfaces, possibly inside the camera as well as outside. To stop this, you should seal up your gear before you go inside. Best option is a sealed plastic 'zip lock' bag...but if you just keep the camera in a zipped up camera bag and let it warm up gradually before you open the bag, that is better than nothing.