In the Painting An Old Man and His Grandson by Domenico Ghirlandaio it shows the old man with bumps all over his nose and face.
Is this a specific condition of any kind or is it an artistic statement or what?
Looks like rhinophyma, advanced rosacea on the nose.
ETA: Son of a gun, guess which painting is on the Wikipedia entry for rhinophyma. 
The painting was central to the “Renaissance Faces” exhibition that has just finished at the National Gallery in London and the clear consensus amongst art historians is indeed that it’s rhinophyma. For example, Brian Sewell’s review.