Here's a snippet from an email list as received Tuesday:
"I've been up at MK for the past five days and snow is melting fast...road is open to Eagle Lake Trailhead...some flooding at Monarch Creek crossing. High country still full of snow with dangerous to impassable creek crossings. I'll keep you posted, Karl "
Mineral King Sub-District Ranger
Sequoia and Kings Canyon National Parks
EDIT: This just in from the same mail list:
I just spoke with the ranger and was told that the road is open all the way to the end. Cold Springs is closed to vehicles right now but is open to walk in camping. Sounds like there is still a descent amount of snow in the campground and the roads in the campground are pretty saturated.