Italy itinerary in March

If you like Baroque, I'd suggest Turin from Milan. For Florence, if you never have been to Sienna, that would be my top suggestion.

Ooh, didn’t know about Turin, I’ll research. We stopped in Siena on a previous trip, so would want a different town or tour this time.

In Milan you can spend quite a lot of time in art museums. I'd suggest digging into those before firming up the number of nights you want to spend there.

I haven't been to Turin yet, but I have a long list of Art Nouveau buildings to see there. I'm looking forward to spending over a week there at some point.

The weather was decent for me when I went to Rome in Feb/Mar 2023, but I was bothered by the short days (which situation noticeably improved by mid-March) and was well aware the temperature didn't get up to 40F until around noon. One thing I did differently on that trip (my only visit to Europe outside the May-October period) was take a full-length raincoat in addition to my packable rain jacket. I didn't use the coat very often, but I was very glad I had it. The coat fit in my suitcase on hotel-change days.

Have been several times in March and temperatures were not severe, with some very nice days, as well as some rainy days. Have also experienced quite cold and blustery days but we were in the mountains, which isn’t part of your itinerary. I always take a warm jacket which doubles as a raincoat and therefore saves space.

I feel pretty good about my Eddie Bauer Girl on the Go trench. I spray it with waterproofing before trips. That and a good hat should get me through.

It’s a good point about the art in Milan. I might not actually have time for any day trips from there.

Frankly Milan doesn't deserve three nights, in fact consider deleting it.
Stick to the big three, Venice, Florence and Rome.

Rome need way more than three days.
There is a great high speed train from Venice to Florence and then to Rome.