A few winters ago we spent New Years in Italy with some Italian friends. They invited us to tag along on their trip to the chic ski town of Cortina in the Italian Alps. While we didn't ski, we spent our days playing in the snow, wandering downtown, and eating lots of great Italian food. The town is quaint resort town full of skiers, relaxed food joints, and scenic vistas like the one above. This trip was really memorable for us, as we stayed with a friendly Italian family and a bunch of fun Italians (Francesco included) and got a peek into Italian mountain living that we would have never have gained access to as a "tourist."
If you're interested in planning your own trip to Cortina, you can start your research at Wikipedia or here. We got to be passive travelers with our friends planning all the transit, but keep in mind that you'll pile onto a coach bus with a bunch of noisy tourists for the long, slow ascent into Cortina. This isn't a hop on the train and get to your destination type of trip.