Why does my nose run if I cool off too fast ?

If you cool off fast, the blood vessels in your body constrict very quickly (similar to what they would do if you go outdoors in cold weather). This happens in your sinuses, too. Since the linings of your sinuses are mucous membranes, and are HEAVILY fed by blood vessels, when the vessels contract, the liquid from the blood pes that barrier/membrane, and your nose runs :-)