Leavenworth [1] has its own tiny ski area, Leavenworth Ski Hill (509/548-5115), with two rope tows providing uphill transportation for the handful of runs. There’s also a snowboard half-pipe. The ski season here is generally shorter than at the bigger areas because of the lower elevation.
Two larger ski areas are close by: Stevens Pass [2], 35 miles to the west on Highway 2, and Mission Ridge, 35 miles in the other direction near Wenatchee [3]. Mission Ridge is a favorite of locals because of the dry snow and less-crowded slopes.
Links:
[1] http://www.moon.com/destinations/washington/north-cascades/leavenworth
[2] http://www.moon.com/destinations/washington/north-cascades/stevens-pass-and-skykomish-valley
[3] http://www.moon.com/destinations/washington/columbia-gorge-and-wine-country/wenatchee