Kids need to be supervised so that any signs of frostbite or hypothermia can be spotted immediately. Proper hydration is often forgotten in the cold weather, but is still important. Your body still loses water when you exercise, even in the cold.
Remember to have a "buddy" or someone who knows where you are going and when you should be back. Then if you run into trouble someone can get you help.
Fresh air and exercise can be fun in the cold, just be sensible. Sometimes a day at the gym is the best choice........