Well, Minnesota's winter is world-wide famous--big snow, freezing temperature, thick ice--sounds scary, huh? Haha, don't be scared, even it's cold here in the winter, people still have lots of ideas of having fun. ;)
I went to ski a couple weeks ago--it was my first time and it was fun! (though I was very bad at it, lol) The place I went to is called Welch Village, one of many ski resorts in Minnesota. They have professional equipment which can provide you safety guarantee. They also offer classes for different levels--don't worry if you are a beginner or even have never skied before, like me, you can go to the class and learn it from very experienced coaches!
Indoor--Concerts, Play, Dance
If you are not a big fan of outdoor activities, you definitely can stay inside--sip some coffee, grab a muffin, and enjoy some art! There are many indoor places you can go to find wonderful shows, with student discount (very important, lol)--Northrop Dance, Guthrie Theater, Walker Are Center or just random coffee shop or bars with band playing music.
Hope you enjoy the life here beyond study! Stay warm, and love you!