agnew meadow late June

too early to answer your questions about Donahue.
ask again in late March or April.
chances are there will be at least some snow that time of year, even in a low snow year. you should be able to follow tracks and cairns.
but whether you'll need crampons/ice axe … too early to tell.

Last summer, 4th week of June, I went over Kearsarge, Glen, Pinchot, Mather, Muir, and Silver passes. All except Muir were mostly snow free.
But 2013 was an exceptionally dry year.

So far it is looking like a la nina year – low precipitation. But sometimes it isn't anything and the sierra get hammered in late march.

However, so far so good. :-)