I personally think Venice is better during the winter months. It is less crowded and there is a wonderfully peaceful and atmospheric ambience with the low winter light and frequent fogs.
December and January with their frequent cold and sunny days tend to be marginally drier than November. I have spent the whole of November twice in Venice, the first time it rained a lot, the second time hardly at all and the weather was glorious. In January, some restaurants and hotels close for a week or two. However, there will still be plenty that are open though.
I would wholeheartedly recommend giving yourself this wonderful experience.