Hi Sir or Madam,
What breed is your dog?
Has your dog's nose changed color at all?
Any nasal discharge?
Could it possibly have been from hot food?
It's possible your dog's nose area is getting sunburned, wind burned or dried out from your air conditioning system. You can try putting some Vaseline on it, which will help moisturize and protect it. But there is also a condition called discord lupus that describes what you are seeing as well.
Here are links to sites with more information on discoid lupus.
It might also be hyperkeratosis as well. You might try Kerasolv ointment and see if that has an affect. It can be caused by hypothyroidism, an autoimmune problem, fungal disease, a bacterial infection, or nasal mites
If the area has been moist, then it is possible that a skin infection may have developed in the area such as a yeast or staph dermatitis. If you suspect a yeast dermatitis, miconazole cream on the area may help control the dermatitis and allow the area to heal.
I would plan on having this looked at by your vet and have a skin scraping done to rule out mites and check for ringworm which is also a possibility. You can read about that here:
You vet may prescribe antibiotics as well. I hope this information is helpful to you.