Don't know for sure, but with the current snowpack, I doubt the road will be open very close to the trailhead. At the very least, you won't get past Scatter Creek, which should be rushing very high this time of year, assuming you can even get that far. Check with the ranger station.
I'll coming from NC out Memorial week and am trying to line up a few areas. The road to Tucquala Meadows is closed. I Iooked at the Enchantments and the road to Eightmile should be open as of yesterday. Hope to climb Shuksan and Baker as well. The road to Shannon Cr is open almost to trailhead. The road to Mt Baker vista is open to mm 5.7. The road to Johannesburg is open to mm 21 though not sure how far in this is. These areas seem like the only really accesable areas this time of year. Any other recommendations in the Cascades, east or west side? I'm traveling a long way and want to have as many options as feasible before I arrive. I've had pretty good weather on my 5 trips out in the PNW although last year it was borderline crappy on the West rib of Jeff but good on the east side of the Sisters. I have posed this inquiry to a few knowledgeble people on SP and have looked at CC as well. Thanks
PM sent. Short version: the PNW is notorious for having shitty weather on any given three day weekend. Follow the good weather, which is typically better on the East Side. You specifically mentioned Johannesburg Peak. EVERY active Cascades climber has a story about epicing on J-Berg.