Woops, little late on this one, but will reply anyway in case other people read it. There is indeed water at trail camp. I saw someone else on a similar day say the lake was frozen over - there were a couple frozen lakes near trail camp, but there was also a smaller body of water, I guess you could call it a pond, of non-frozen fresh water where we and lots of others were filtering water and refilling their water supplies. It's between a bunch of rocks near trail camp, so I could see how one could miss it if they walked to the outside of it. But look around, and there is indeed water!
Wind was pretty calm - we checked mountain forecast for Mount Whitney which suggested 5-10mph winds, which seemed pretty spot on. The weather was supposedly mid to upper 30's at the summit, but with all the hiking I was pretty warm - didn't even don my jacket until the way down after the chute, just had a long sleeve shirt on with long johns and waterproof hiking pants that I had put on to keep my pants from getting wet.