This will depend on where in the Dolomites you plan on going. If you want to go to the eastern end near Cortina I would go to Venice first. If you are planning on going to the western side near Pinzolo or Trento then I would perhaps consider going there first. Also, consider that you are going in December so you may encounter bad weather. If you are going to Venice first the train is an easy way to get there and then from Venice you can rent a car or a driver to get to the Dolomites. If you want to see the western side of the Dolomites you can take the train to Trento and then rent a car. Anyway, you look at it, to get into the heart of the Dolomites to experience all its beauty you will most likely need a car at some point.