The closest skiing is at Mt. Charleston, about 45 minutes drive from Vegas....
The hill, which changes names often, is now known as "Las Vegas Ski & Snowboard Resort".
See their website at:
http://www.skilasvegas.com/winter/index.html
It is actually a pretty cool place to ski....when there is enough snow. Very dry, powdery conditions compared to most places on the West Coast (Sierras or Cascades), with maybe a dozen (15?) or so runs, and never any crowds on weekdays; although you may actually have to wait in a lift line on weekends.
Although it has been several (many) years since I last skied there, I have always enjoyed it, and it is quite a refreshing and scenic diversion from the Valley.
Generally they try to open around Thanksgiving, snow permitting, and the season lasts through February (March in a good year).
