Our noses are warm and humid and as we breath in cold air it goes into the lungs. When we exhale that is when the moist tissues in the nose kick in automatically to increase fluid production to do its job of protecting sensitive lung tissue. that's about it I'm afraid.

Think of an ice cold drink on a warm day... the moisture in warm air condenses on the glass as the energy is dissipated from it(like dew; this is how clouds form around dust particles (condensation nuclei). When you exhale warm, moist air from the lungs on a cold day it condenses onto the nasal tissue and hair as they are colder than the air warmed by the lungs. One of the functions of the nose is to warm inhaled air to protect the lungs, thus cooling the nose.

Chris, not the sort of topic to think about over dinner. Take a handkerchief.
I totally agree with Strider. There might be the addition of latent heat energy also, hut I cannot add to the above comment otherwise.
Nothing wrong with body fluids.
.....and I am happy that whatever our knowledge, we can never fully understand nature.

ShropshireLad: Why don't noses run on the same routes in Summer then?

Warmer air?
So, warmer nasal tissues, plus warmer air can hold more moisture.
So, wipe in winter only🙂

One thing's for sure....sinusitis sufferers get through faaaar too many packets of tissues during the Winter!🤔

Wow - thanks everyone - nose drips have been a favourite and lengthy conversational topic of mine for years as my friends can testify - it is great to see this topic out in the open 😋

Wet noses run in our family🙂

I usually find that my nose is running constantly when walking on the hills. Then, on other occasions not, for no apparent reason. A head wind makes it run. However, if you are getting over a cold, a day on the mountains is great for clearing you sinuses.