For some reason walking in the snow is much more fun than walking not in the snow. Think about it..."What did you do this weekend?" a) "me and my friend went for a walk" or b) "me and my friend went snow shoeing" Who knows why, but it is more fun. Crosscountry skiing is even better if you have the legs / butt for it. Plus MN was built from Norweigans / Swedish, so you probably have to try it once. In the summer you can go for walks or bike.
A good site for outdoor activities in MN is Explore Minnesota
Price: $7 (for snow-shoe rental)
Location: See: MN Trails
Cheap and fun things to do around Minnesota/St.Paul