Drive your own dog sled through the snowy wilderness or over a frozen lake. We've gone mushing with Snowy Owl twice and highly recommend it. They offer pick up/drop off service from your hotel. Book in advance as they often sell out!
Hit the slopes with Ski Big 3! The lift tickets are good for all 3 mountains in the area (Mt Norquay, Sunshine, and our personal favorite, Lake Louise). The have flexible use dates and include a shuttle to/from the mountains each day. If you order in advance, the tickets will be waiting for you at your hotel when you arrive.
If skiing is not your thing but you still want to see the breathtaking views of the Canadian Rockies, take the Banff Gondola to the top of Sulpher Mountain. Walk along the top of the mountain and enjoy the views or even grab a bite to eat at the Sky Bistro. If you book in advance online you can receive a 10% discount!
A short drive outside of Banff, the waterfalls of Johnston Canyon freeze in the winter and make for beautiful scenery. While we haven't done the icewalk ourselves, it has been highly recommended to us every year. You can rent snowshoes and explore on your own or go with one of the many guided tours.