Aug 15, 2016 - 3:08 PM
Welcome to MySwissAlps!
1. For the best chance of snow fall, you should be high up in the mountains. Towns like Zermatt, Saas-Fee, Mürren and St. Moritz would qualify. There are no guarantees, but your chances will not be good in a town at low altitude like Lucerne. If there is no need for you to be surrounded by snow, Lucerne will be just fine and you can visit some peaks as day trips for your snow experience. It is a lovely scenic town with lots to do and see.
2. You first need to have a fixed itinerary. Then pick a pass based on that. This is a good starting point: myswissalps.com/ train/ ticketspasses.
3. I would skip the Rhine Falls in December. It's not the most attractive time of the year. The train you mentioned is called the Bernina Express. You could stop for a day in St. Moritz.
Does this get you started?