The weather is being unseasonably cool, so you will encounter nearly the same conditions. With microspikes, you can walk down -- hiking poles (with snow baskets) would be especially helpful.
Understand that later in the afternoon, as the day cools and the slope is shaded by the mountain to the west, the slope can become icy (depending on the temperatures). So you should try to get down no later than 3 PM, and earlier would be better.
HST (High Sierra Trail) info, NOT the Mt Whitney trail: Are you sure you can negotiate that tunnel and snow in the narrow chute above Hamilton Lakes (at 9300')? It can be pretty treacherous when the trail is covered by the winter's snow.
Here... I did a google images search for "hst tunnel hamilton lakes", and found this picture and post by RoguePhotonic:
Quote:
Your biggest concern with snow is going to be the tunnel section as you drop off or climb the Kaweah Gap. If you have any gear you will be fine but in 2008 in mid June I had to spend 2 hours digging a level trail through the snow because it was hard packed and steep. One slip means death in that spot.
Notice the cut in the snow:
You might want to consider carrying an ice axe and crampons, just for that particular spot.
