April 20, 2000, left Kennedy Meadows on June 1, and ran into just enough snow to make some people nervous. But we had fun with it. 2000 wasn’t a particularly high snow year so there was only 3-4 miles of snow before and after each of the passes. Only Forester and Mather Passes and the fords at Evolution and Bear Creeks were really tricky. We lost it and got wet at both of the fords, but then we needed the baths by that time anyway. 
But the most dangerous part was the snow blindness that developed when Ginny didn’t use her sunglasses one afternoon. That cost us two days at Vermillion Valley, but even that was sorta good cause we got to spend those two days with Butch and Peggy.
Yogi’s right - snow and ice “can” be dangerous. But what’s REALLY dangerous is hiking “by rote” – as in actually believing that a “set date” like “leaving KM on June 15” will guarantee safe passage. The June 15 date is an artifact - a mantra - that originated with some of those who were too lazy to actually read Jardine’s book and figure out what he really said. The actual “safe” date varies considerably, depending on the winter snowpack and spring conditions. We left KM on June 1 and hit high snowmelt - those who left KM a week later barely got their feet wet and had clear passes and very little snow. We have friends who left KM on June 1 in other years and never walked on snow the whole trip. And other friends (different years) who left KM on June 15 and hit massive snowpack and truly dangerous stream crossings. It depends on the “year” – the snowpack and snowmelt conditions. So don’t get lazy - do your research or you might be unpleasantly surprised.
Actually, though - I’m not a believer that there is any real “safe date”. I agree with Pappy that if you’re gonna hike the trail, you need to learn to deal with the mountains on their terms - not yours.
Jim