Recent reports of the Mountaineers Route have stated that most groups are leaving all the snow gear home.
Reports from the main trail still suggest crampons and Ice axe can be useful while on the switchbacks if it is early or late when they would still be icy. Some are taking the snow gear but not actually using them.
You will need to get a day hiking permit if you go up the MR.
Here are some recent photos of the MR, taken on May 25th.
http://outdoors.webshots.com/album/559215127sCZiEN