All types of batteries use a chemical reaction to produce electrical power, and the speed of a chemical reaction is affected by temperature. As the temperature drops the reaction slows down, which means that the battery produces less electrical power, and as it runs down it will quickly pass the point at which it is no longer produces enough power to run your camera. A 10-degree reduction in temperature can mean as much as a 50 percent reduction in battery performance, which means that your camera will run out of power very quickly when it gets cold. Different types of batteries are more or less susceptible to this effect. Cheap copper-nickel and older Ni-cad rechargeables are affected the worst, but even high-power alkaline batteries and modern Ni-MH rechargeables suffer from severely reduced performance in cold weather.
Lithium and Lithium-ion rechargeable batteries are affected the least, which is good news since most modern digital cameras use this type of battery. If your camera runs on AA batteries, I strongly recommend buying Energizer Lithium. Not only do they last up to seven times longer than alkaline batteries, they are half the weight and are much less affected by cold weather.
In order to keep your camera running in cold temperatures, it's a good idea keep a spare battery or set of batteries in an inside pocket under your outer layer of clothing, where they'll be kept warm by your body heat. When the battery in your camera starts to fade, swap it for the warm one and carry on shooting. You'll find that warming up the cold battery will restore it to life, so you can swap the two batteries over several times.
For really cold conditions, separate external battery packs are available to fit many cameras which can sit in the warmth inside your coat supplying power to your camera via a cable which simply plugs into the DC power socket. Some of these require a dummy battery to be fitted, but it so it will usually be included.