This is too late to be of use to you but answering so others can find it in the future -- yes, generally Palazzo Vecchio is one of the few museums/sights open, the other one being Palazzo Strozzi.
We always update this for the next holiday period by the start of December, so check it out to see what is open during the Christmas season in Florence: https://www.visitflorence.com/christmas-holiday-museum-hours.html
It has opening hours for Palazzo Vecchio and Palazzo Strozzi and any others we find will be open on the specific holiday dates.