Do you have 14 nights in Italy, not counting the night on the plane or the day you fly home? Typically you need 2 nights in one place to have a day between to see something of the place where you're sleeping.
Regardless of the transportation you use, 7 places with only 14 nights is really not enough time to see or experience much of the places on your list, much less do any day trips -- unless your trip is about the driving or train riding and not about being there.
Of the places you list, Florence is not the only place where parking might be a hassle, especially considering that you might not be allowed to park in some of those towns at all, much less close to where you're staying or for free. Some of them are hill towns where parking is below and you have to walk your luggage up and down stairs and steep slopes.
Don't count on the Italian weather being similar to that of Greece in December. My experience has been that it's colder and wetter. Do check the averages and recent year data online. And don't forget that the days will be short and some places may close earlier than you might expect.
If you haven't done so already, take a look at this free downloadable brochure What you should know about renting a car in Europe in 2019 on the Gemut.com website. There's lots of great info on both the renting part and the driving part. There are many special rules about winter driving.
There's good info on this RS website in the Travel Tips: Transportation. Drill down in those tips to find details like these Driving Tips and Road Rules
Driving in Italy is not for the faint of heart or the low budget traveler. Postings about getting tickets in Italy are commonplace. This very important paragraph is from the driving tips linked above:
"Car traffic is banned altogether in many Italian city centers, including Rome, Naples, Florence, Pisa, Lucca, Siena, San Gimignano, Orvieto, and Verona. Don't drive or park anywhere you see signs reading Zona Traffico Limitato (ZTL; often shown above a red circle). If you do, even briefly by accident, your license plate will be photographed, usually without your knowledge, and a hefty ticket — or tickets, if you did it multiple times — will be waiting for you at home."
The ZTLs alone provide tickets for many and keep many others from driving in Italy. Oh, and make sure you have a current International Driving Permit (IDP).