I think you have too many places on your list for 10 days. If it were me, I'd take advantage of it being low tourist season and spending 3 days in Venice, 3 in Florence and 4 in Rome. High speed trains connect all 3, and I wouldn't consider any of them good cities for tourists to bring cars - Venice because you literally cannot have a car in the city itself, Florence because you will get a ZTL ticket (and the city is compact and easily walked), and Rome because it's more or less thunderdome.
We were in Italy last Feb and spent 8 days in Florence just kinda hanging out and not waiting in lines to see things. It was great, and very different from a crowded summer stay. I'm determined to do Venice that way too.
Weather's cool by my standards in those cities, but it's also 12 degrees right now where I'm sitting in Portland, Maine. So going somewhere that it's in the 40's and 50's in the winter is just fine by me.
Now, if you've seen all of those places and really just want to drive around in a car, I say go for it. In that case, my advice is to avoid the cities, since you can't bring your car anyway. Make it a tour of the winter countryside.