My best friend and I did Langley last June and it was very clear of snow. The only snow was a 10 foot cornice on NAP that we ended up bypassing by scrambling over some class 3 to the side. This June, especially with the low amount of snow, I highly doubt there will be any snow to worry about on NAP.
However, when we went to OAP to check it out it was completely snowed in and unfeasible unless you had axe and crampons, as wbtravis said, so unless you have the gear and experience, I would just plan on NAP. OAP is quite steep and climbers have died on it so proceed with caution. The mountain will always be there, and the additional 1.5 - 2 miles are worth the safety.
There were a couple snow fields near the summit that were full of suncups and penitentes but they were also easily passible, since the majority of the summit is a scramble.
I would love to add pictures of the trip, as I well documented it, but I'm not sure how to insert from iPhoto. If I'm told how, I will share the experience!
