Can fat be extracted from the nose?

There really is only an extremely tiny amount of fat in the nose and most of it is "tied up" in with other tissue. Sometimes in a "fat" nose with thick skin and a lot of fibrofatty tissue under the skin, in addition to other maneuvers, we may CAUTIOUSLY thin a bit of that layer from the underside of the skin for a bit more refinement. This only contributes a tiny bit to the overall result.

There is no fat located in the nose. The rhinoplasty procedure involves reshaping cartilages and bone underneath the skin covering over the nose. For many examples of rhinoplasty, please see the link below

Although a majority of people don't have a lot of fatty tissue in their noses, some do.  Removal of cartilage and skin can help achieve a more narrow look but, when necessary, some fat may be removed as well.