Yes, expect all small towns across the region to be open, including shops and restaurants.
Many are small but still have locals living in them year-round so will be open, although quieter than usual.... expect shops to be closed at lunch time, as is still common practice.
The only ones which will seem a bit deserted in this period are the ones right along the coastal area, since they depend a lot on summer tourism... this includes Elba, although it does have residents/locals in the off-season.
If you head to the mountains above Pistoia and the Abetone area, or to Monte Amiata between Maremma and the Val d'Orcia, there should be skiing once more snow comes (if you're interested ;-))
If you stay in the central area of Tuscany - Chianti, Florence, Siena and Val d'Orcia - you'll find everything open.