The most facile explanation might be that our African ancestors, on moving north, encountered colder air than they were adapted to, and suffered accordingly until it became an advantage to inherit a nose long enough to warm inhaled air before it harmed the inner respiratory system. I have little doubt that this will have been a major factor in the ancestry of my glorious nares.
However, there are many counterexamples. The Oriental and Eskimo snub noses would seem to be cases in point, not to mention the Finns. Part of the difficulty of finding a convincing general explanation is that there probably is no people on Earth today whose ancestors have had a single, stable territory throughout the past five or ten thousand years, so the adaptive influences have been changing hither and yon all the time.Even the climate has been varying confusingly in various directions at various times and places.
My guess, and it is no better than handwaving, is that some of our ancestors moved so far north that long noses became a greater frostbite hazard than could be justified by its limited air warming benefit. A frozen nose would not be much good for warming air anyway. But so many people have wandered from pillar to pole and back again so often, and have been subject to so many influences, including xenophobia and sexual selection, that the best way to tell who is talking nonsense might be to assess who has the greatest air of confidence.
Errr... I think....
Jon