I have been up in the area many times in late May. Usually the snow path is well worn by then and easy to follow. In a heavy snow year (like this year) there could still be snow down to about 10,000 feet. Early in the morning the snow is hard enough to walk on top. During the middle of the day sinking in can become a problem if it is warm and sunny. If you don't have snowshoes, do your travelling early when the snow is still frozen. Only one year when we had June temperatures the second half of May did we wish we had snowshoes.
Above trail camp you will probably take the snow field up like every one else. On the back side of the mountain (above trail crest) there will be drifts but often not that much snow.
Crampons/ Ice axe and perhaps even snow shoes can be helpfull, depending on how warm it is. I would not think a helmit and rope would be necessary. There are no crevasses on the trail to fall into. Falling through is not usually a problem, unless you are walking off trail over a snow bridge covering one of the rivers.
It is a great time of year to be up there. Take a look at Bob R's photos, taken in middle May up the regular trail.
http://members12.clubphoto.com/robert634908/1310304/guest.phtml