This might sound odd, but if your body becomes so warm that it begins to sweat, it will make you even colder than you were before. The easiest way to cool off is to bare your head, neck, hands and wrists as they are the areas where body heat is lost the quickest. Exercising will help your blood flow, but don't allow yourself to break a sweat. Another concern with exercise is the possibility of over exertion. When the weather is cold, your body, and especially your heart already have to work much harder to maintain body temperature and over exertion in the cold weather can even be fatal.
Many people die from heart attacks each year as they shovel the snow from a storm.
If shoveling snow isn't critical, don't do it. If you must shovel snow, don't overexert yourself.