Luckily the Rawah's are one of the few places the DOW hasn't ruined with it's "stock G-Backs everywhere " program. The DOW goes in and murders perfectly viable populations of macs,browns,bo's,snake river cutts,and brookys to stock weak,vulnerable greenbacks. Who the hel& wants to catch greenbacks in EVERY high lake? A little variety is a good thing. The only reason for stocking greenbaccks everywhere is that they tend to reproduce so the DOW saves money by not having to stock every few years. Many of the lakes they stock with "native" G-Backs never had any fish at all. A bunch of B-S if you ask me.
I have spent quite a bit of time up there the last few summers. I wouldn't bet on them being open much before July. Some of them start opening earlier depending on the weather and elevation but I have made some long hikes to find snow and ice at the end of June. But if you're like me and like to get out for a hike in the high country, start checking them out in mid June, you might get lucky and find open water.