Utah has a LOT of things to do, year-round. There is much mor in the summer than the winter.
Start with just the incredible mountains. Behind Mount Timpanogos (Provo and Orem), there are various natural springs that have been made into parks. Climb any of the mountains. There is excellent cliff climbing behind the Provo Temple. There are extensive dinosaur fossils in the NE part of the state. Bear Lake in the north, and Lake Powell in the south both offer all sorts of sports. The canyons in the SE are incredible, especially Zion and Arches.
There are hot spring resorts tucked away in various places. If you time things right, you can see events on the Bonneville Salt Flats. Visit the Golden Spike National Historical Monument.
Then, for LDS, and other interested parties, there are all sorts of historical sites. There are even a few "mystical" sites to be visited.
Utah is a great place to visit, as well as a great place to live.