I hiked from Cottonwood Lakes to the Mt. Langley summit via New Army Pass on June 22nd, 2018. The trail was completely walkable and snow-free until the top 10 feet, which required a simple scramble to avoid a small snowbank. My friend and I did it with full backpacks without issue.
Old Army Pass was covered in snow and was not walkable.
Mt. Langley was entirely snow-free. The last few miles to the summit are incredibly challenging - basically an uphill slog on gravel and scree.