You can certainly do a loop trip from Milan and back, if Milan is your key arrival/departure point.
And I’ve been in Florence twice in November - really nice, but certainly cooler than there in the summer! Maybe a bit cooler yet, in December.
This may be too far-flung for a trip starting and ending in Milan, especially without at least a second week for traveling, but we had a 3-week trip in December 2012-January 2013. We started in Rome before Christmas, but the city was decked out for the holidays, including a giant Presepi (manger scene) outside St. Peter’s Basilica. We took a quick, cheap flight to Sicily, where we spent Christmas. We then returned to the mainland, and had a festive New Year’s in Sorrento, south of Naples. Day trips from Sorrento included Naples itself, and the surviving ruins at Pompeii and Herculaneum. We finished with a train ride to Rome for our flight home.
If you’re interested in an Ancient Roman Empire town site, and don’t make it to Pompeii or Herculaneum way south of Rome, visit Ostia Antica, just west of Rome. It served as the port of Ancient Rome, and surviving bits include a tavern that seems like they could open up tomorrow and start serving food and beverages again, part of a mansion with amazing floor mosaics, and a large public toilet that’s amazing, considering that Roman plumbing was state of the art, 2,000 years ago. Maybe more comfortable and efficient than a restroom you’ll find at a modern arena or public gathering place nowadays.