IdEaMaNi, that picture, the last on the previous page posted by Philippe (View from Trail Crest) does not look like a storm to me, but rather just clouds or fog. Granted, when the area is fogged in, you can't see far, and you get zero views, but it isn't necessarily stormy.
Today's webcam shows the summit under clouds, but then checking the Doppler Radar for Lone Pine (link on the Mt Whitney Weather page, above on the left), it shows the area is not receiving any precipitation. There IS some precip north and south of Whitney -- at least 10 miles away, but the clouds on Whitney are not dropping any moisture.
When planning for a trip, you should look at the various weather forecasts linked on the Mt Whitney Weather page, and make your decisions based on what they predict.
