It is impossible to diagnosis this without biopsy BUT ...
My best guess would be that this is a cutaneous fungal infection caused by a group of fungi that cause tumor like growths.
The location on the nose would make my guess more feasible because squirrels root around in the dirt. Molds live in the dirt. Rooting around in the dirt with a possible 'side order' of frostbite and/or suppressed immune system due to the stresses of a very hard winter could set this little guy up for a fungal infection.
The specific groups are called Phaeohyphomycoses or Chromoblastomycoses. WARNING : I wouldn't be googling images of these unless you have a strong stomach.
These molds are ubiquitous but you rarely see them in people in developed countries.
http://en.m.wikipedia.org/wiki/Phaeohyphomycosis
http://emedicine.medscape.com/article/1092695-overview
The other possibility is of course a malignancy but I do lean towards a fungal cause.
Unfortunately, neither will be treatable if this is what it is.