[Nose][1] is a serious filter, pre-heater and humidity conditioner for the air. It is full of hairs that trap larger particles that are often germs or allergens. It moves air through the system of sinuses to make sure it is warm and humid enough. 

If there is enough air passing through the nose, it is healthier for other parts downstream to have this filter machinery engaged. This is the most true if it is cold, dusty or very dry. Of course, if so much air is required that it all cannot pass through the nose, nothing to do.

Also, the referenced source says that the cold air may cause the airways in the lung to contract and dry air may thicken mucus there, making the lungs less efficient.


  [1]: https://allergyasthmanetwork.org/news/your-nose-the-ultimate-air-cleaner/