Michigan has so many beautiful trails to hike in the winter months. However, I will have to say the prettiest and the most accessible trails (in my opinion) is the trail to Wagner Falls. It is short so doable for all ages (providing it's not too icy) and it has a beautiful waterfall the end.
Michigan has so many fantastic beaches but one of my favorites is Chapel beach in the Pictured Rocks National Lakeshore. This beach has great sand, stones perfect for skipping, cliff edges, a beach waterfall that you can walk through and just when you think that's enough it has a very cool rock formation that has a beautiful tree on it whos roots traverse air to get to the shore to survive. It is a pretty special place. Oh and you can only get there via boat or a long hike.
Michigan is very lucky to have so many beautiful state parks and I know I have just scratched the surface of these parks. One of my favorite thus far is Silver Lake Sand Dunes State Park in Mears, Michigan. I love that the winters change the dunes each year and that the change also reveals these interesting stumps