Hogadon Ski Area, on Casper Mountain (just 10 minutes from the city) offers 24 downhill trails served by 3 ski lifts, and 600 vertical feet of terrain for snowboarders.
Of course, Hogadon has bunny slopes, intermediate and advanced slopes, including some black diamond trails. (Bunny slopes are ID-d by green circles, blue squares mean intermediate, black diamond is for advanced skiiers.)
The Casper Nordic Center, also located on Casper Mountain, offers cross-country skiing day and night. In addition to the lighted, groomed track, there are 50 kilometers of backcountru and snowshoe trails.
Hogadon also offers a ski school.
The resort building is located on the summit of the mountain, as opposed to the base, which is pretty cool.
In order to keep up with Hogadon - during the snow season, of course, check out the Hogadon Ski Report, here: http://www.skireport.com/wyoming/hogadon/
