I'm not exactly sure on the snow depth. I live at a lower elevation, 2500'. At 7000' there is still over 10 feet of snow. So at Kyburz, which I believe is around 4000' - 5000' there could still be plenty. It's getting warm so hopefully it will melt quick. But the shady areas tend to take a long time. You should at least be able to partially head up that road. Or if you head south on Hwy 50 you could probably find some decent roads at a lower elevation. On that link I posted there are some USGS maps you can download.
The Rubicon is a pretty serious trail. I have a stock limited so I didn't venture out too far. I did the first climb onto the granite face and took the picture.
Have a great trip