Although there are no designated cross-country ski trails, once snow falls--sometimes as early as October--the park becomes a winter playground, especially at higher elevations. You can use cross-country skis or snowshoes on many of the trails and several roads, although it's best to talk with rangers about your plans before setting out so you can avoid trails that might be too steep for your ability. In lean snow years you may have to hike a bit from parking areas to snow that's right for skiing, but there's almost always plenty of snow at the higher elevations.
One favorite cross-country ski trip is up Baker Creek Road, which leads to Baker Creek Campground, and then on up the Baker Creek Trail for a while before heading back. Those particularly skilled and in good physical condition might ski the 4-mile trail from Upper Lehman Creek Campground up to Wheeler Peak Campground. The trail climbs about 2,100 feet. Although Wheeler Peak Campground is technically closed from about mid-October through mid-June, skiers are welcome to spend the night.
There are no snowshoe or cross-country ski rentals available in the park or nearby.