I would think white truffles in Piemonte and Le Marche would be an occasion for food tours in December. I wouldn't expect them to be cheap -- but you never know!
In some parts of Toscana and Lazio in early December the new olive oil is pressed.
There is scarcely a month in Italia where some town isn't having a food celebration: Chestnuts, pumpkins, artichokes...
What is your itinerary?
In Romagna, you know, Pellegrino Artusi was born, the father of the Italian cooking recipes. Well, in his born town, Forlimpopoli, between Cesena and Forlì, there is a very clever cooking school named, you can imagine, Casa Artusi.
Here it is possible to tast the true typical Romagna cooking and learn how to make piada and few other very typical Romagna dishes.
In which part of Italy are you coming ?
If you're coming in Emilia, I suggest you the food tours enabled by Antica Corte Pallavicina, a very charming D&B, whose patron Massimo Spigaroli is a very clever chef and in December there are special events focused on "bolliti".
Anyway, it is the right month to taste here also Culatello di Zibello DOP.
If you're coming in Marche, I can suggest you several places where perhaps it is still available to taste truffle and, for sure, porcini mushrooms.
If you're coming in Romagna, December is the right month for the local fresh fish and for the filled handmade fresh pasta.
A good referral blog could be http://ilcommensale.san-lorenzo.com/