During winter, you may or may not find snow on the floor of Yosemite Valley, but Yosemite Falls is nearly always flowing at least a little.

Winter
(December through March)
A season of snow & solitude

Areas to visit: While Yosemite Valley and Wawona remain accessible by car all year, the Tioga Road is closed (usually by sometime in November). Once closed for the season, vehicles are not permitted between Crane Flat and Tioga Pass, including in the Tuolumne Meadows area. The road to Glacier Point is also closed (usually sometime in November). However from mid-December though early April, the Glacier Point/Badger Pass Road is plowed to the Badger Pass Ski Area, where both downhill and cross-country skiing are popular. Tire chains are often required on park roads. When they are, you must carry and know how to use them, regardless of the type of vehicle you are driving.

Weather: Winter in Yosemite is snowy and cold, though sunny and chilly days are not uncommon.
Yosemite Valley & Wawona (4,000 ft / 1,200 m): 53°F (12°C) / 28°F (-2°C)

Rivers & Waterfalls: Water levels tend to be low, but once some snow and rain have fallen, Yosemite Falls begins flowing again (though not at springtime levels).

Hiking: Most of the park is covered in snow during winter, but some trails in Yosemite Valley are often accessible. Backpacking options are very limited.