There have been several recent threads on this subject.
I was in the Sierra a week ago. Having been in the Sierra (mainly summer, but some winter) for over 50 years; following Sierra snow reports; reading Sierra long-range weather forecasts; etc., it appears this will be a low snowfall year, but "low" is a relative term.
2012 is a La Nina year, but 2011 was also a La Nina year. Last winter, Arctic Oscillation, predicted two weeks out, prevailed and resulted in very heavy snowfall. There is still time for a "Pineapple Express" condition to set up and dump significant snow.
March, April and May (yes - May) often are significant Sierra snow months. Total snow is part of the summer "hike ability" equation - the other part is snowmelt: when melting starts, snowmelt rate, etc. Snowmelt also determines mosquito hatch.
Last year, snowmelt started late April/May and then snowstorms with cold weather would arrive and stop the melting process. Last summer, high passes were snowbound well into July. I went over Forester Pass mid September last summer and hiked through snowfields.
Consider starting at Yosemite and going over high passes later in your hike; more time for snow, if any, to melt. There are many threads on this subject: day hike from TM to Happy Isles, etc.
Late June is better than early June.
Do not bring crampons and ice axe. By early/mid June, PCT through hikers will have cut defined paths through snowfields, if any. In the unlikely event snowfields are frozen, just wait until sun softens the snow.