Minnesota has a great network of state parks, and there's still plenty of activities at the parks even in the winter!
If you want to try something new, some parks offer rentals of snow shoes or cross country skis, plus just snow hiking, which would be on hard-packed trails so you don't need any special gear.
Be sure to bring water with you in the car and dress in layers. Don't forget sunscreen, the snow can be bright! Check out these parks if that's something you're interested in trying:
(this would be a longer drive, but worth it!)
Minneapolis and St. Paul both have lots of activities to explore! We don't go often, so don't have specific suggestions, but there's lots of museums and parks to explore. Also, the Mall of America! This is a great website to check out for more ideas: Explore Minnesota
Minnesota has a great craft beer and cider culture, plus a lot of great restaurants. A couple of our favorite spots are The Uncommon Loon Brewery in Chisago City and The Garage in Pine City. The Uncommon Loon does not serve food so we recommend getting take out from either The Northern or The Stone Inn next door (a couple more restaurants high on our list), and The Garage is a full service restaurant.