Florence in January -

We spent 3 nights over a weekend in Florence a few years ago and loved the lack of crowds! Yes, it rained some but we also had some good walking weather. We also were able to grab a room at almost half the high season rate in a nice hotel. Restaurants were uncrowded as well and we felt the proprietors were relaxed and welcoming as so few patrons were around.

Transit strikes in Italy are announced and seldom last long. This site has been dependable for me to check what’s happening. https://www.summerinitaly.com/traveltips/transport-strikes-in-italy

Our visit at the beginning of January was many years ago but the weekend we were there it was sunny and in the 60s. It was totally pleasant. An unpredictable time of year. Probably most likely to be chilly and showery -- but for us the sun shined. Florence is a nightmarish oven in the summer, hotter than even Rome. Given the choice I'd go with risk of cold and showery. Much of what makes Florence worth visiting is indoors.

Check out daily weather conditions in Firenze on timeanddate.com for January this year and the last 10 years too.

January is generally the coldest month.
You can check the forecast for the next 10 days and also monthly averages online.
No strikes in Italy.

We assume you are asking about Florence specifically, and not Tuscany in general.