Since it is unknown what the weather will be between now and early June it is not possible to say exactly what you might encounter. However, one thing that I would recommend you do is browse the trip reports for hikes done in Late May to Late June. You will likely encounter conditions similar to one of those previous hikes. Most trip reports have photos, and some even have video.
Go to Trip reports, and you will find they are arranges in chronological order (newest first). Jump down to page 5 or six, and you will find May/June of 2014. Check those out, and then skip back to 2013, 2012, 2011, etc... 2011 might be a good "frame of reference" since that was a similar snow year to this year.
Of course you best information will be from trip reports just prior to your hike. Just keep checking as your date approaches.
Good luck.
