Just got back from our excellent adventure in Young Lakes. Went in via Dog Lake Trail, went out via Soda Springs trail. For those interested, TR is as follows:
Snow is minimal until the Dog Lake side of the loop connects with the Soda Springs side of the loop. At that point (the last 1.5 miles to Young Lakes), the snow was patchier across the ground, but nothing too serious. It covers the trail in a number of spots, but there's lots of bootprints to follow across the snow until it rejoins the trail. We never were worried about getting lost. At Young Lakes, there is plenty of dry ground to camp on, but also many remaining patches of snow and a lot of muddy snowmelt as well. The lower two lakes are unfrozen, but Upper Young Lake is still partially iced over.
Stream crossings were manageable. Dingley Creek was crossable via rockhopping - we didn't get wet. Delaney was wadable - it was up to my knee at the deepest point (I'm 6'0"), but not too fast. Basically an easy crossing that none of us had any problems with. (This was the case with Delaney across both branches of the trail).
Mosquitoes were out in force. Bring repellent, head nets, and loose fitting clothing. I've got about 20 bites, most of which were through clothing. Certainly annoying and unpleasant at times, but not so bad that it ruined the trip by any means. Just be prepared.
I'm not sure about Tuolumne crossings, but it looked pretty full from what little I saw of it - we didn't make it to Glen Aulin or beyond.
Overall, a great trip, great hike, well worth the visit.