Ckgor, there is a major storm currently all over California, except for the southern part. Check the weather links on the Mt Whitney Weather page (see the link on the left.) If you go to Mt Whitney, you will experience nothing but cold, wind, snow, and NO views. The mountain is completely lost in clouds and snow. Look at the web cam views.
If you get into the middle of that, you could get turned around and not be able to find your way out. Not even the most experienced mountaineers would venture into that. Bob West is right: Come back in summer!