Be ready for snow. I just checked the snow sensors, and this weekend was a wet one. As of 7AM today, the Chagoopa Plateau sensor was reporting a snow depth of 92.7" with a water content of 14.29". 59% of this came this weekend. And Chagoopa Plateau is in the rain shadow of the section of the Great Western Divide that includes Black Rock Pass.
Perhaps a better indicator of conditions at Black Rock Pass would be the sensor at Farewell Gap at the southern end of Mineral King valley at 9500'. As of 10 AM today, it is reporting water content of 28.62"; the snow depth sensor is giving a funny number (maybe due to heavy snow still coming down) but I would estimate it to be around 140-160". Black Rock Pass should be close to that.
The storms will continue through Wednesday, although not as strong as what rolled through this weekend. It has been raining all morning here in Visalia. The snow line is fairly high, averaging around 7000' or higher. Even if you only go to Bearpaw, there should be plenty of fresh snow. The Mineral King Webcam shows good winter conditions, and it is at the same elevation as Bearpaw (7820') and not far south of it.
http://www.mk-webcam.net/Even the Giant Forest webcam, which is at 6620', shows lots of snow
http://www.nature.nps.gov/air/webcams/parks/sekicam/sekicam.cfm