Cat's noses will peel much like people's skin does, although it takes much more severe sun, wind and rain to make it happen.
There is a product called "bag balm" that's a moisturizer. You can get it at wal mart. It works great for cat noses and for the bottoms of the feet.
If there are wounds or mucousy/goopy areas on the nose, you can clean the nose with peroxide or betadine and then apply some neosporin ointment. If this does not help, you will want to see the vet for an antibiotic.
Aside from that, thyroid conditions can cause unknown nose and foot problems so you will want to have your vet run a thyroid panel to rule this out. Some people have to go so far as to tattoo the nose to promote healing.
Let me know if you still have questions.
Sometimes a wound on the nose can start the ball rolling. Then it just gets worse. I would try the peroxide/neosporin/bag balm routine and see if it helps. If not a vet visit will be needed.