I was up there last weekend on my Bike and the Gate is still closed. I made it up to the Fork for Mineral Basin and Heber before I was riding on packed snow.
They usually don't open it till around Memorial Day, so you have about a month still.
Memorial day is the usual opening day, it really just depends on the amount of snow still on the road. They check it out and make sure that the road won't be extremely damaged from the moisture before opening it up. As I recall last year, it was opened the weekend before Memorial... I can't wait...