Winter can be very nice or very difficult to visit Yosemite. There are fewer people, fewer campsites available, fewer rooms, and much of the park may be deep in snow (see the Tuolumne page for more on that). This leaves the Valley and Wawona (and Badger Pass for skiing). At 4000' the valley floor is usually snow free, and roads are quickly cleared (though the days it snows can be slushy). Compared to Sequoia and Kings Canyon, Yosemite is somewhat easier and more predictable in the winter.
It is important to remember that winter conditions in California are controlled by the storms from the Pacific (or Gulf of Alaska). With no storm, it is clear and sunny, with a storm it can be heavy rain and/or snow. Plus, the type of precipitation depends mostly on elevation. Rain in the valley, snow on the valley rim. Or snow on the valley floor, rain at the entrance station in El Portal. It is hard to plan far in advance, but if the forecast is for no storms, there will be no problems. So, don't stay away, but be aware of the conditions, both current and for the next several days. Driving can be a problem (with or without chains) during and soon after the storms, but for much of the winter the patches of ice are the greatest danger. The lowest elevation route into the park is via CA 140 (El Portal, originally called the all-weather highway). Wawona to the Valley goes much higher is more likely to have snow for longer periods.
If you define winter as snow, April is as more winter than November or early December. But in April, the valley is barely freezing and the roads become slush by afternoon. Usually there are no problems later in the day, once the snow has stopped falling, but mornings can be icy. Roads are plowed and the shuttle and tour buses use chains, but no salt (or other chemicals) is used.
One big question is when does winter start and end? It varies, but the high roads (Tuolumne and Glacier Point) usualy close in November or early December and reopen in May (or June). When depends on the exact snow fall. The snow depths in the backcountry usually peak in April. Closing dates depend on how early the snow starts, opening dates depend on how much snow fell that winter. Early closure does not mean late opening nor does late closure mean early opening.
Winter sometimes brings snow to the valley floor. The 4000' elevation is low enough that it will not last long so enjoy it while you can. | The falls usually are flowing a bit more than the late summer minimums, and also have ice buildup (generally it can be 5-10 deg colder at the top of the fall than the bottom (in whatever temperature scale you want to use)). | Winter lasts longer than you might expect, April can still seem like winter with fresh snow in the valley and ice on the falls. |
All the views from the valley are still there, with different lighting and clouds. | And depending on the day and weather, you get very different views. | Mirror lake is much more in the shadows all winter so it retains light snowfall longer than the other meadows. |
You can experience several seasons in a week in April. | Snowfall is not common, but can come at anytime. | The cold cuts the flow. | Sunshine after snow fall is one of the best times. |