White Mountain Road to a bit past Crooked Creek Research Station should be open by June 1, at least to those with real (not toy) 4WD and suitable tires. That is, via the bypass road that initially leads to Wyman Canyon, then cuts back to White Mountain Rd, circumventing the 10600' hump of White Mountain Rd (blocked by heavy snow drifts in many places). Road conditions are extremely risky for tires (cuts and punctures from many small sharp rocks)—the worst I’ve seen in 10 years, so take a real spare tire, not a blowup spare. This will apply even in summer—the rocks are very nasty for two miles or so leaving the pavement at Schulman Grove. Low speed even for A/T tires to reduce the risk of cuts.
The crew from White Mountain Research Station are hard at work as seen below. As for whether the road to Patriarch Grove will be passable, it’s hard to say—I could not get far enough to see into the dip area just below Patriarch. But the road above Patriarch will surely not open for weeks.