Not true only in Florence of course, but International Women's Day or the "Festa della Donna" on March 8th is widely celebrated in the Tuscan capital, and the Florentines have their own unique way of celebrating this event:
"Traditionally the women are given a small bouquet of mimosa - yellow flowers in a small cluster, that emit a sweet fragrance, and spend the evening without male company."
The Festa di San Giuseppe (St. Joseph's Day) is celebrated on March 19th in Florence and across Italy. Although it is no longer a national holiday, it is now also Italian Father's Day (Joseph being the father of Jesus of course!)
March 25th is the historical date of the old Florentine New Year, which of course is not officially recognized now, but still celebrated in the city. It is also the date of the the Festival of the Annunziata, also known as the Feast of the Annunciation, which takes place in Piazza Santissima Annunziata, and commemorates the announcement by the Archangel Gabriel to the Virgin Mary that she would conceive and become the mother of Jesus Christ.
While it may not be high season for tourists, there is still plenty to see and do in Florence in March - and if the above events are not exactly what you are looking for, then the museums, churches, piazzas, and shops of Florence are always there to keep you busy!