Any snow-covered hill around town can be used for tobogganing. Locals will tell you to visit the Spray Meadows Hill behind the Banff Springs Hotel or the Cascade Ponds on Minnewanka Road. Both sites are unsupervised so please have fun, but take care.
Toboggans and sleds can be rented or purchased in town if you were unable to fit one into your luggage.
Snow tubing is a whole lot of fun. It is similar to tobogganing, however instead of having to trek to the top of a hill after riding down, a plush towing system will do the hard work for you. As you relax back while being pulled to the top, take in the fresh mountain air and views before hurtling back down again. Tubing is a great activity for all ages, including children over the age of 4 (or 42 inches tall).