Yes, FREE first Sunday is not part of Italian Culture Ministry policy so it shouldn't be going away soon.
Even though winter is low season, the museums still get pretty full on that first Sunday when lots of locals go too. As Donna suggested, I would recommend taking advantage and visiting the smaller museums - such as the Bargello, San Marco, Medici Chapels - on that Sunday and leave the Uffizi or Accademia to another day. In your case, that would be the day before since you only have the weekend. You might not need to book ahead of time, given the low season.
It is impossible to BOOK tickets for the free Sunday - it is museum policy to not give preference to anyone and let everyone get in line to enjoy the museums.