I hate when my nose and ears get cold. I use a balaclava or a kufiya/shemagh to keep my face and nose warm.
This nose warming thing is goofy looking but I dont think it's the worst idea ever. We have fluffy goofy earmuffs and no one gives those a second thought or glance. Is a goofy nose warmer really any different? Besides scarves and balaclavas and kufiyas all have the same problem. Your breath creates moisture behind the scarf and collects causing the scarf and the face to become damp after prolonged wear. That cant happen with these nose warmers. And if it does it only effects the nose and not the whole lower face.
I work outside 40 hours every week year round, and I learned years ago that staying warm in sub freezing temps is far more important than looking cool and sensible while doing it. So yeah I'd wear a nose warmer if it worked and I'd shrug off anybody that gave me shirt for wearing it, because I care about staying warm and avoiding frostbite and chapped skin.