I'll add to this: my group hiked the Whitney trail on the 28th and 29th, two of us with crampons and axes planning to summit and two with just microspikes and poles. The two with spikes decided to stop at outpost camp mostly for fatigue, so we decided the other two of us would climb up more for fun, but plan to camp at outpost and not summit. The trail between outpost and mirror lake was quite covered in snow, and was passable with microspikes for someone with experience moving around snowy slopes, but crampons were very much preferable. Much above outpost, I'd say you can progress without crampons, but only if you're very comfortable on winter terrain.
I'll second the caution about buried rivers, as well. We noticed lots of post holing into flowing water when the snow got warm, though mostly didn't experience any ourselves. Most of it was into shallow minor washes, but there was the hiker who died just above outpost camp a few days ago when the snow gave out into a major flow: http://ktla.com/2017/05/24/san-marino-wo...heriffs-office/
