You'll be able to rent a sled (snowmobile). Artic Cat dealer west of town & Polaris dealer east of town should be able to fix you up. Snow shoeing, Cross Country Skiing. Check out Stub's Museum Bar.
Camp One Store on the main street usually has some pretty decent buys on outdoor clothes.
Not sure if you'll be able to get into Porcupine Mt. State Park with a vehicle. The hike on snow shoes would be worth the trip to see the view of Lake of the Clouds.
About 1 mile south of the junction of M107 & M64 is a little side road that leads to the falls on the Big Iron river. It's a short 1/4 mile walk.
Good food at the Konteka restaurant in White Pine.
If you are driving, make sure you stop at Lawry's Pastie Shop on M28 west of Nagaunee. Buy a dozen regulars that are cooked & frozen for gifts