Dog's noses will peel much like people's skin does, although it takes much more severe sun, wind and rain to make it happen. Under the black skin of a normal nose, there is fresh, pink skin. With time, this skin will darken and "match" the rest of the nose. Abrasions are commonly caused by rubbing the nose on a crate or pen door, on furniture or even sniffing concrete.
There is a product called "bag balm" that's a moisturizer. You can get it at wal mart. It works great for dog noses.
If there are wounds 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 problem 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.