'Cold' is a matter of what you're used to.
You can reassure your parents that frost or snow in November is very, very unlikely anywhere in Italy
other than the highest mountains. It'll be chilly in the mornings and after sunset but temperatures will rise during the day. So it's really just a matter of packing clothes you can layer as required (e.g. sleeveless t-shirt under t-shirt under shirt/blouse under fleece/sweatshirt/jersey), hat, scarf & gloves plus warm waterproof/water-resistant outerwear and sensible footwear which is comfortable for walking (by far
the best way to see any European city) and will keep your feet dry if it rains. It's best to have outerwear with a hood because umbrellas are a real nuisance in cities and frankly useless if it's windy. But do take sunglasses too (Italy can be sunny even in winter)!
Imo, November is an excellent time to visit Rome
(or anywhere else in Italy). Although there will still be plenty of visitors you'll miss the hordes who visit in the warmer months, hotel rates will be lower and everything you need (sights & sites, places to eat etc etc) will be open. The only real downside to a winter visit is that daylight hours are shorter than in the summer.
I'm not really sure why you want to add Milan
? Although it has some interesting historical sites and sights it's not on most people's lists for a first (or even second) visit to Italy. Why not choose Florence
(site map shows Firenze S.M.N.
(two of the 'top three', each absolutely and entirely different both to Rome and to each other)? If you want somewhere not in the 'top three' I'd suggest you consider fascinating (and foodie) Bologna
, with its historic upper and lower towns, Como
, with its options for exploring the lake settlements, Naples
which is stuffed with history and has easy access to Pompeii
and Capri, Italy
...or base yourselves in La Spezia
and use the cheap, frequent trains to explore the Cinque Terre
Personally, I'd visit any or all of those places before I visited Milan...and I did, though I've now been to Milan too. :-)
Getting to all the places I've mentioned by train (some high-speed, some not) is absolutely safe, very reasonably-priced and very easy indeed even if you have no Italian at all. You can check train times, details and fares in English on the official Italian railway website: https://www.trenitalia.com/en.html
Another company runs high-speed trains on some of Trenitalia's high-speed routes, using much the same stations and charging similar fares:https://www.italotreno.it/en