Why does my noise stay cold?

Blood flow. If the blood flow to your nose is not great, your nose can feel cold. Remember that as an "extremity" with thin skin that protrudes from your face, some coolness of your nose compared to other, more central body parts (like your cheeks, forehead, or abdomen) may be normal for you. If your nose becomes discolored, blue/dusky, or is numb see your doctor right away.
Less blood flow. Unless you are my pet dog, this can suggest circulatory issues. Does your nose change color. There are types of circulatory conditions that causes a nose to be cold and turn blue or white. I am uncertain this is the problem. The nose is far from the central body temperature control and peripheral areas of our body will divert blood flow to the central blood flow = hence a cold nose.