We went up Gorgonio June 12, via South Fork Trail, leaving overnight gear at Dry Lake about noon and making a straight line up to the summit from the saddle above Dry Lake. No snow until just before Dry Lake, where it was patchy (plenty of dry ground to camp), then on and off up to the saddle, and all snow from there on. We took the middle shute, hugging the trees on the right, and found it not unlike the snow slope up to Trail Crest. Very steep near the top, but hiking pole or stick and crampons were sufficient--left ice axe behind, and didn't need it. Snow slushy and melting fast, so conditions have probably changed much since then, although early morning could be slippery.
NOTE there WILL be volunteers checking permits on the trail as early as 8am (needed for both day hiking and overnight), so call ahead or plan to get there early enough to pick up permits at Mill Creek Ranger Station (they open at 7am, and leave permits--1st come, 1st serve--out overnight for early morning self-registration, if you are just hiking, not camping.
Bugs (annoying but not biting) will probably be out in force by now, so a head net or repellant might be good to have at lower elevations. Have a great hike. We did.