Lisylu, read the topic just below yours. Some think it was not a serious post, and maybe I'm getting pranked here, but this thread has the info you need covered very well.

http://www.whitneyzone.com/wz/ubbthreads.php/topics/23212/1

Yes, there might be snow in places year-round, but the trail opens up at some point in time - usually June. This year was a lower than average snow year, but late May is still early season. You will be on a snow trail in places, but there should be lots of clear trail - but probably wet. If an ice ax is needed, it would be due to the 97 switchbacks being snowed in. If that's the case, then you should either have an ice ax & crampons and know how to use them, or turn around there at Trail Camp (12,000 ft). Coming down the chute from Trail Crest to Trail Camp can be dicey, people have gotten out of control and died there.