This isn't very useful as I've never been but I'm planning to try to summit in July. Never been up that high so not sure how the altitude will feel. I'm going to be exploring the Bristlecone pines so I figured we'd head over and try. Plan to camp at the gate to help acclimatize and try to summit the next morning.
There are more details on summitpost http://www.summitpost.org/white-mountain-peak/150221
and in Zdon's desert summits book http://www.amazon.com/Desert-Summits-Climbing-California-Southern/dp/1893343022