Why is your nose always cold?
The tip of your nose extends out from your face, and its surface area/volume is high (which means that this is a large part of your face on the outside, but has a large empty cavity on the inside). The effect can be cold skin. Your nose also comes into contact with the outside environment quite often (more often than many other parts of the face or body), and doesn't have much insulation, which means it can't resist temperature change.
It seems that way (perhaps it is just a little cooler because the cool air goes into that part of the body). If your mouth were open to breath instead of your nose, then your lips would be cooler too. If you touch other parts of your exposed body, it seems cooler outside than you feel inside.
Not necessarily. About 2 years ago i was always cold, nose hands, everywhere, and it turned out to be an underactive thyroid. I am now on daily medicine for that and, my nose is still cold all the time. Maybe if the rest of you is cold all the time, and you have low energy and your skin is dry, you could get your dr to have a blood test taken to test your thyroid…