I did the Mountaineer's Route the 1st weekend of June in 2014. There was some snow, but nothing we couldn't handle in micro spikes. We had crampons, but never had to use them. Last year was a dry year and this winter was even more dry. I'll post pics if I can get it to work.

(Went up the MR and came down the traditional trail.)

Here's a link to pics:

https://www.flickr.com/photos/52913270@N02/sets/72157645103435925/