lesper4,

Snow levels go up about 500 ft/week this time of year in the Southern Sierra's. So in 3 weeks the snow conditions can be completely different. It's hard for me to predict that far out. I would estimate the snow level at this time to be around 11000'.

If I was going from Horseshoe Meadows to Whitney Portals I would go over Cottonwood Pass (~11140') instead of New Army Pass (12310'). It is more likely to be clear of snow by that time and the total distance is about the same. Then, your main concern would be the 99 switchbacks below Trail Crest (~13700'). Keep checking the message boards to see if they are passable by then. Good Luck and be safe!