JOJO, not sure about the road -- I think they try to get all the roads open by May 1. But you can call the Inyo County roads department at (760) 878-0202 in Independence and ask.
The snow around Cottonwood Lakes is over 3 feet currently. You can see the
Snow depth graph at Cottonwood Lakes, elev. 10150' link on the
Mt Whitney Weather link above on the left.