Even then people were taking tours of the salt mines as the visitors do today. The largest ice caves of the world are another major attraction south of Salzburg.
You may go jogging in the 17th century park of Hellbrunn, walk up a mountain right behind your house, or take public transportation to the nearest ski resort. In the winter, there even is a "skiing train" that takes you directly to a lift station. A great opportunity to meeting Austrian skiers.
In keeping with the weather conditions, Salzburg College offers a Skiing course during the spring semester and a Hiking/Rafting course in the fall. Staying overnight in a mountain cabin is a great experience after a long day's hike.