Exercising in the cold creates a unique set of challenges.
The primary concern is keeping the body warm, both in the core as well as the extremities. When temperatures drop below 40*F, wind can make temperatures feel colder than they actually are.
As the body loses heat to its surroundings, the air immediately around the body acts as an insulator which helps the body stay a bit warmer. Wind blowing across the body removes this layer of body warmed air, which in turn increases the sensation of cold. It also causes the body to work harder to maintain a normal core temperature. Wind also increases the efficiency of evaporation which is a cooling process; sweaty skin or clothing exposed to the wind will cause the body to chill more rapidly than it otherwise would.
The combination of cold temperatures and wind speed is known as the wind chill factor. The colder the temperature and/or the faster the wind speed, the lower the temperature will actually feel. In some cases, the wind chill factor can be low enough that exposed flesh can suffer from frostbite in less than 30 minutes or in extreme circumstances, less than 5 minutes. Areas most prone to frostbite include extremities such as fingers and toes as well as portions of the face. The other concern when faced with cold temperatures made still colder by the wind is hypothermia. Hypothermia is a dangerous lowering of the core body temperature which can lead to very serious complications including death.
The best way to combat the cold is to dress appropriately for the combination of cold and wind (wind chill factor calculator: http://www.hpc.ncep.noaa.gov/html/windchill.shtml), limit the time spent outdoors, or find an indoor place to exercise.