A healthy nose secretes about 32 ounces of mucus every day. This doesn’t tend to make your nose run; most of this mucus falls to the back of the throat and is eventually swallowed. These secretions help to humidify, warm up, and filter incoming air.
Why?
Only so much of it can fall to the back of the throat and be swallowed. When mucus and secretion production increases to warm the air, you will see the nose run because you have excess secretions. In other words, some of it has to drip out the front because you have an excess supply.
What can I do about it?
Wrap your nose and mouth with a scarf when outdoors. Breathing through the scarf will warm the space between your face and the scarf. You will also exhale moisture into the space which will moisten the air. By warming and moistening the space, your sinuses won't have to produce as much moisture and your nose will not run.