Winter coat in March?

Layering is best to deal with a variety of weather conditions. Make sure one layer is a good waterproof jacket. Have something warm to wear under it if necessary.

I wouldn't go too heavy in March, especially the end of March, unless you plan to go at high altitude and the cities you mentioned are all just above sea level. Of course nobody can predict weather too far in advance, so I would check the weather forecast just before traveling. That should give you an idea of the weather in the following 10 days. Generally March has a high probability of rain, therefore more than a heavy coat you should consider a rain jacket. Temperatures are generally cool in the mornings and evenings, but not so cool that you need a heavy coat, so layers are a better strategy, because in the early afternoon you would probably have to take a heavy coat totally off.

At that time of year, the weather can change dramatically from week to week. We were in Rome once, in mid-April when the high temps were in the 40's. People told us the previous week had seen 70's. Do check the forecast just before departure. A rain-resistant outer layer over a wool cardigan should see you through a wide range of weather. Remember that gloves, a hat, and a scarf (warm, not decorative) will add immeasureably to your comfort if it's chilly; and they take up very little room in your luggage.

The free App
iL Meteo
shows temperatures and weather conditions in Italy for two weeks. Search for the cities you will visit. Quick Convert Celsius to Fahrenheit by doubling Celsius and adding 30.

We had January weather the middle of April two years ago, and June weather in March. Weather is weather! Bring a rain jacket as Roberto advised, and layer. Wear your heaviest on the airplane. I bought silk undergarments from an on line ski apparel compay and used it in the really cold weather. Agree that you should check the forecast a day or so before departure.

an unlined fleece jacket.....one of those that the collar can zip all of the way up and be a turtleneck....would be even lighter weight and easier to carry around than a wool sweater....