Speaking as someone with a long slender nose, I have my doubts about it moistening dry frosty air. During the Winters, the only thing my nose seems to be good for is producing blood and dried mucus wafers like some cursed Triscuit factory.
It's not about your nose. It's about the relative differences of the air reaching the lungs when inhaled through different nose. You may not think that your nose does a very good job (or perhaps I picked a wrong example), but perhaps the job would get done much worse by a short wider nose.
Some environmental parameters are temperature and absolute humidity. But there are also significant differences in sex when a other parameters are equal. So perhaps the correlation is not so straight forward.
I can see that. Contrary to my personal feelings about my own nose, having grown up in a more Northern latitude where Winters were much, much harsher than what I experience now, there was a few key things I learned at an early age that stuck with me well into adulthood.
Breathing through your nose in the cold while walking to class was one of them. I heard this a lot back then, the logic being as you propose; that it just gives the cold air a bit more time to warm before it reaches your core. Adding to that, you were also supposed to breathe slowly, rather than taking fast, gulping breathes. That just added to the reasons to avoid over-exerting yourself in the cold, which poses other risks.
Other stuff had more to do with choice of clothing material, layering, etc, but that's not really applicable to this conversation.
Interestingly, while it still does get cold where I live now, nobody really pays attention to these rules. I'd say the difference between the two areas is something like -5F on average, give or take. I am not sure how significant that is.
> Breathing through your nose in the cold while walking to class was one of them.
After extensive nasal surgery in 2009 this became an option for me again, after over 20 years when it wasn't.
I discovered a less-discussed rider: yes, it seems gentler on the lungs to breathe in through your nose in sub-zero weather, but there is a condition: you should breathe out through your nose as well.
Exhaling warms the structures in the nose so it can warm the next inhalation.
But, for me, that same sub-zero weather often causes my nose to make more mucus -- so breathing both in and out means a lot more use of a handkerchief, or a nasty snotty moustache.
Honestly, all this makes zero difference if you're not frail or in advanced age. I regularly experience winter temperatures of -30°C or lower (-40° is not infrequent), and it really doesn't matter how you breathe.