The following excerpt is taken from
http://www.drgreene.com/21_650.html
and explains a bit about what might be going on when your nose runs from the cold . . . both mucus and condensation are to blame.
"Breathing cold air can also trigger nasal congestion and wheezing. Sometimes this is a purely physical effect. This happens in two ways.
First, cold air affects an important defense mechanism called mucus transport. The entire respiratory system is coated with a very thin mucous blanket. Cold air stimulates an increase in mucus production, but mucus (like other substances), becomes thicker in colder temperatures.
The second area where cold air physically affects respiratory health is in the nose tissue. The hardy nose is a remarkable organ designed to condition inhaled air to protect the delicate internal structures. When breathing through the nose, you may breathe in air at 40 or 100 degrees Fahrenheit, but within a quarter of a second, the air temperature is quickly brought to 98.6. Many tiny blood vessels, known as capillaries, bring about this temperature exchange. When a person breathes cold air, the tissues lining the nose swell as the capillaries dilate, bringing warm blood to heat the cool air. Swollen capillaries in the nose are the cause of nasal congestion (nasal congestion is backed-up blood, not increased mucus). In addition to the congestion, the mucus in the nose, as we've said, increases and becomes thicker. This happens more in some people than in others. Thus cold air, by itself, can produce both nasal congestion and stuffiness. These can be treated with decongestants and/or antihistamines. "