The nose is a furry creature’s conduit of affection.
A cat has glands along the side of its face, around the upper gums, and as they grow comfortable with you, they’ll want to incorporate you into their olfactorial environment by rubbing these glands into you. If they’re especially affectionate, they might rub into you very firmly, even pausing, letting the heat from their gums warm your nose. It might sound weird at first, but, who are you kidding… just let the furry thing do what it wants to your face.
The scent wears off though, especially after a shower, so this ritual becomes construed as “morning greeting” as smell is restored. Sometimes, they’ll clean off your nose themselves, just so they have an excuse to nuzzle you again.
Word of warning though. You can’t assume they’re always in the mood to nuzzle you. I tried to get a picture of the one of many nuzzles Luna gives me in the morning, but I almost got my nose chomped. It’s a mild version of Russian Roulette, where you might win, but you might also suffer the humiliation of a scratched nose. If I see you, and you have a red line near the tip of your nose, don’t think I don’t notice. I know you have a cat, and I know what your cat did to you.