It is still winter and the crowds are thin, the squares a bit more quiet - until Carnevale blows into town (although you are really supposed to go to Viareggio for the full effect). This year (2014) Carnevale actually comes in March!
February is also a great time to taste new wine - both Benvenuto Brunello (date not yet set) and the Chianti Classico Collection (February 18th and 19th at the Stazione Leopolda in Florence) happen in February.
Tickets can be hard to come by (and you may need to be in the wine business or a member of the media) for both events so if you are interested start looking into them now!
There are also a couple of fairs on tap - a nine day Chocolate Fair in Piazza Santa Maria Novella, and the one day "Fierucolina dei semi" or "Plant and Seed Fair" in Piazza Santo Spirito featuring vendors selling plants, flowers, seedlings and more. Sunday the 16th from 9 AM until 7 PM.