BK,
The Mt. Whitney region is generally not considered one of the better backcountry skiing areas in the S. Sierra.
That said, lots of people try to ski Whitney each year, for the same reason they hike it -- because it's the highest peak in the continental US.
The trail crest route Richard mentions probably offers the best skiing, though conditions almost always rule out connecting the summit.
The MR chute is an aesthetic descent, but be aware conditions above the 'notch' to the summit (the north chute) are life threatening, and should not be attempted via skis unless you have a good deal of experience in high-altitude, no-fall terrain.
-- maybe not even then.
As for avy info, check out the eastern sierra avalanche center:
http://www.esavalanche.org/ Andy
SierraDescents.com