Lake Placid has actually hosted the Winter Olympics twice (the first time was in 1932) and is well known for both its alpine and Nordic skiing opportunities.
The ski resort of Whiteface claims to have the "greatest vertical drop east of the Rockies" and with 85 trails and 314 acres of skiable terrain, there's certainly plenty of snow.
Real thrill seekers can even join a professional bobsleigh driver and brakeman and ride the Olympic bobsled track.