Hey Herf!
You and your wife must be thrilled! I hope you guys have a fantastic time!
Of course, March will probably be different than when I went in December.
Like you, I used The Weather Channel or https://weather.com/weather/tenday/l/ITXX0067:1:IT It can display averages, but nothing is set in stone when it comes to Mother Nature, lol.
Before my first trip to Rome, I went on a couple different sites to view the average temps for two weeks.
The first trip to Rome, it was freezing and windy walking around. I was glad I wore a winter coat. It reached "maybe" 40-45 degrees F most days at peak (45° being generous.) On windy days, it seemed colder. It rained a bit on one or two days, nothing serious. At nightfall , it dipped.
My second trip was a surprise. Rome was very mild, humid/balmy (for the same time frame.) A few days reached mid 60's+ (at peak.) People were saying it was unusual for that time. Most days were maybe 50's? Spring like.
Coming from the East Coast, flying in December, I wore my coat and accessories. But, of course wearing/layering thinner clothing underneath can be helpful; adjust accordingly.
The first year, I wore my wool, winter coat. Walking around Rome, it weighed on me; even though I appreciated the warmth. Last year, I wore my thinner, but warm puffer coat. On warm days, I just left it unzipped. As the day wore on, I appreciated having the coat, scarf and gloves though. But, I'm always cold! lol.