We spend a few days in the area last weekend. There is no problem with the snow up to Upper Boy Scout lake. The approach east of UBSL to the Saddle is mostly clear, as is the canyon above Upper Boy Scout lake via the Rockwell variation. There are some snow drifts in the canyon but not much to worry about. Early in the day you might need crampons for a short section. The Russell Carillon saddle has some snow but it is flat up there and you could walk over it or go around it. Look at the Thor peak pictures on May 30th from SBC. Especially picture #21 and #24
http://www.whitneyportalstore.com/cgi-bin/ubb/ultimatebb.cgi?ubb=get_topic;f=1;t=001995
From the East summit of Mt. Russell, we took a good look at the East Arete approach to Russell. There is snow filling the crack during the most exposed area, where you are closest to the cliff. I think that could be quite dangerous unless you were experienced and had Ice Axe and crampons for just that area. There is also a 30 foot snowdrift just east of the east summit, but that wouldn't stand in your way.
I would recommend the Route taken by Bob Rockwell
http://members12.clubphoto.com/robert634908/1422442/guest.phtmlThis route is safer and mostly free of Snow. We went via Iceberg lake which ends up at the same place once you get above the Whitney Russell pass. The South headwall route was a nice one with good handholds. We took along a rope but left it at the bottom of the headwall once we took a close look. http://www.whitneyportalstore.com/cgi-bin/ubb/ultimatebb.cgi?ubb=get_topic;f=1;t=001870
The southheadwall route comes up in the middle between the east and west summit. The east summit is easy to get to. The West summit requires dropping down 15 feet or so on the North side about half way there.