According to an article on teenkidsnews.com, the nose is responsible for filtering out all the bad things that could make us sick, and ensuring that the lungs stay moist and supple.
When the temperature drops, the nose begins working overtime to add humidity. This reaction—called rhinorrhea—can be almost instantaneous. Step outside into the chill, and a river will start to flow down your nose. The nose compensates for the change in temperature this way by producing more mucus and more liquid to keep the nasal tissue hydrated and moist. It is the same system that causes the mouth to water in anticipation of a meal.
The second cause of a cold-air-induced runny nose is simple condensation. The air inside the nose is kept at about 36°C, and when that warm air comes in contact with cold air, the reaction is moisture. That condensation—which is really water—joins with the mucus and adds to the outward flow.
This flow may appear endless, but it will generally be a thin flow and is not the same stuff you see when you have a cold. Because this fluid has to keep the nasal tissue and the lungs moist; thick, heavy mucus simply won’t do the job because that will merely just block the lung tissue.
Some of the nose’s primary activities include heating the air and mucus production, and usually, only one nostril is wide open at any given time while the closed side does the work. Every four hours or so, the two nostrils switch, with the closed side opening and the open side closing. The warm, humid air is then sent to the lungs which provides the lung with moisture because without moisture, the lungs will constrict and become damaged.
Those who breathe through the mouth will usually experience a sore throat – brought on by dry air – because they bypassed the nose and its lubricating function. But in cold weather, breathing through a scarf or bandana will help the nose do its job and cut down on the outward nasal flow.