The reason your body produces and reproduces snot so quickly is because your body releases histamines which is a chemical that inflames your nasal membranes and causes them to produce a lot of mucus or snot.
So when you have a cold or allergies the histamines can increase which then leads to an increase in mucus or snot coming out.
Cold viruses or even just the cold weather can trigger snot to be produced especially a runny nose because the cold weather or cold viruses can trigger the release of the histamines due to the histamines.
You can help stop a runny nose in the cold by wearing a scarf over your nose to help prevent cold air from getting into your nose.
Also using a saline solution to help clear the nasal passages and using a humidifier in your home or room can help with keep the nasal passages clean and clear of irritants and keep it moist.
Staying hydrated is also another way to help slow down a runny nose.