I'd second Brian Head. It's across the street from Cedar Breaks National Monument, which is pretty reminiscent of Bryce Canyon National Park. It's also an hour and a half from both Zion and Bryce Canyon (both are some of the most beautiful park lands you'll ever see). I think the Grand Canyon is about three or four hours away, but that's the North Rim, which I believe is pretty snowy and limited for hiking in the winter.
Also, Eagle Pointe is supposed to open this season, it's about 45 minutes from Brian Head.
The southern resorts aren't exactly Utah's most challenging or dynamic skiing, but you do get the same dry, desert powder. And some of the best scenery in the world in terms of national parks.
Not sure if you're into backcountry, but Eagle Pointe advertises five bc gates into Fishlake National Forest, and Cedar Breaks has some of the most amazing bc I've ever seen:
In Arizona, you might want to check out Arizona Snowball, which is near Flagstaff and within about an hour and a half from the GC.