You are correct: It has to do with dryness versus humidity, not cold versus heat. That is why desert peoples have large noses. Another half-baked article by yahoo. I’m not sure about all your specifics but the nose is there to hydrate the air before it goes farther.
It also warms and filters the air. Nose hair helps filter out impurities. Many people believe that nose breathing is very important to good health. This may have something to do with why people may have longer noses. Here is just one one countless sites that is interesting about the importance of breathing through the nose and therefore how important the nose actually is. It is possible that Neanderthal with his larger brain capacity and bigger nose was a more intelligent and adept human than we.
http://www.breathing.com/articles/nose-breathing.htm
Nose Breathing
Breathing through the nose has many benefits. Breathing through the mouth, many negatives. There are some researchers who believe that mouth breathing and associated hyperventilation causes or exacerbates asthma, high blood pressure, heart disease, and many other medical problems........