If it snows, it will be a dusting. It will NOT amount to anything that would slow you down, except the cold and the moisture.
You need to check the NOAA weather site links on the Mt Whitney Weather page (link is above on the left). Mountain-forecast.com always over-estimates and over-predicts snowfall.
But you may very likely see thunderstorms. The usually only last an hour or two, and if you have a tent to stay in you will be fine. If you are out hiking, then rain gear is what you will need.
