I was in Palm Desert over the weekend. I could see Mt. San Gorgonio from where I was and could see that it still has a considerable amount of snow. Even Mt. San Jacinto has some snow.
I wouldn't want to climb to the summit of San G. in snow. Too bad you won't be able to climb San G. before you do Mt. Whitney. You would find Mt. Whitney so much easier than San G., except for the altitude (thin air) near or above trail camp.