The gate closure is not far from both trail heads. I think it's much less than a mile.
I was up there on Saturday and yesterday. Cold nights and warm days. Snow is not an issue until almost 12,000ft. I day hiked out of Cottonwood Pass down to Big Whitney Meadow to Johnson Peak. Streams are very small for this time of year. Cottonwood pass is free of snow. Mt. Langley, from my view on Johnson Peak, is pretty snow packed from NAP to the top. NAP has cornice as usual.