You'll be fine at the end of May. 3 years ago was the worst winter we've had (this one might be worse but is turning around and I think it will eventually surpass that year for total snow depth). Regardless, during that shitty winter, Main Chute at Alta was still skiable into late May and June. You might have to do some hiking but it should be too bad. You'll want to stay high elevation for that. By then the snowpack should mostly be good to go, but check out recent observations on http://www.utahavalanchecenter.org
and the Wasatch conditions thread on the tgr forums.
Here are places I would recommend:
Alta: it's not totally "wild" as it's a ski area, but the access snow and terrain are prob the best and most acceptable. Go to Main Baldy Chute (and Little and Dogleg chutes if they are still in) Gunsight on the other side will still be in as well (skied it late July last year) Bonus: depending on what's going on at snowbird, if they are closed for the season, you can take skis up the tram if you sign a waiver, then it is a really easy hike to baldy.
Snowbird:if they are closed and Pipeline is in (it will be), it is well worth the walk from the bottom to hit it IMO. If you're willing for a longer tour, upon exit from Pipeline to west to the White Pine Drainage and look at skiing Red Top or Red Baldy. Red Baldy will have snow. The exit out will lack snow (likely below 8000ft) but there is an easy to locate established trail.
Superior: maybe the south side will still have snow, otherwise the north side will be good to go and have many great options for skiing. Suicide chute will still be skiable. You might have to navigate some rocks and waterfall at the bottom, but that's the fun part.
Uintas: take a drive on the mirror lake highway about 1.5 hours out of Slc. Bald mountain is great and has no approach. There are several other peaks and fun objectives right off the road, which should be plowed by then.
Wolverine cirque: this is tucked between Brighton and Alta. For that time of year, I like the approach from Brighton. Several chutes should be skiable that time of year. You can just pick what you want and go. If seagull chute is skiable off Mt Tuscarora, you have a quick ski over to it from the top of mt wolverine, and a mostly easy exit back to Brighton.
Timpanogos: harder shit but Cold Fusion and Grunge Couloir may still be in. Approach with mtn bike can help for cold fusion. Likely a lot of walking up and down to get to snow but you get to ski a 60 degree slope in grunge (watch for rockfall and do more research on it).
That's about it for the main spots. You can get into some crazier stuff if you're willing to walk a bit. There will be snow up high, it's just about accessing it easily.