I was up there yesterday 6/26.. the only ice was on the switchbacks and then another place I believe is referred to as "the snow field." On the switchbacks, the ice melted by the afternoon (assume this cycle will continue for some more days) and the snow field had openings cut through it so your feet stay dry as long as you don't fall in a slush-hole. You can also walk around this area.
I wore trail runners and they stayed dry, but there are plenty of places to get wet feet if you are not careful.
