The cold air drawn in the nostrils causes the capillaries to contract, which is just a pain... the runny nose is caused by impairment of the cillia in your sinuses. These are little cells with tails that stick out, and the tails sweep mucus back, up, back... and so on. When they get cold, they kinda freeze up and mucus slides all over the place. (Yes, these cilia are the same structures that exist in your throat and get plastered down by tar in cigarettes causing "smoker's cough")
marvelous role of mucus in fighting disease! This ooey, gooey substance is ready to slime harmful germs any time, anywhere by trapping dirt and bacteria that get into your nose or throat! While there's always a thin layer of mucus in your nose, it functions in its full glory when you're sick with a cold. That's when your mucus glands work harder than ever to make extra mucus that will fight off that invasion of extra germs. Hundreds of tiny, moving hairs called cilia also help out in the struggle against sickness. These hairs lie just below the layer of mucus and sweep old mucus and dirt away from your lungs like a broom. The mucus then travels up to your mouth where it's (yecch!) swallowed or to your nose where it's sneezed out. Unfortunately, the surplus mucus can run out of your nose like water through a faucet, too! This slippery stuff will also make your head feel stuffy, but hey--in the long run it's worth the inconvenience.
Even when you're not sick, you may find that your nose is still oozin' overtime! So why does it seem like your mucus glands are still busy making mucus? Well for one thing, they're not! You're getting that disturbing dripping sensation because cold winter temperatures are making tiny water droplets in your warm, moist nose come together or condense. These condensed droplets form big drops that get so heavy that they run right out of your nose. So don't feel like a drip--a runny nose in winter weather is perfectly natural!