Most of the minor roads through the Sierra are closed throughout the winter. Tioga Pass, through Yosemite, is at the highest elevation at nearly 10,000 ft, Sonora Pass not much lower. Here is a list of opening and closings for Tioga Pass and the snowpack throughout the years. You can see how below average the snowpack was during the drought. 1995 was 178% of average and 2015 was only 7% of average. I remember only maybe 10 days of rain during that season.
https://www.nps.gov/yose/planyourvisit/tiogaopen.htm
Clearing of the Tioga Road normally begins on or about April 15 each year and usually takes between one and two months. Predicting when these roads will open is not possible, even in late spring, because April and May weather significantly affects plowing progress. (April 1 snowpack (water content of the snowpack as a percent of average) for the Tuolumne drainage is listed as a reference.)
Here's a video of someone driving 108 in June 2011, probably right after the road opened. They are coming from the east (high desert) to the west. Notice all the starting around 1:00, that's probably near the top, Sonora Pass. 2011 snowpack was 178% of normal.
[video=youtube;4TsMy0fUtFY]https://www.youtube.com/watch?v=4TsMy0fUtFY[/video]