Obviously, it can snow any day of the year up on Mt. Whitney, the nights are getting longer and the days cooler. So winter can come at any time. Often though it snows, then melts, then snows again. I have hiked as late as November 16th on mostly dry ground.
The smaller streams freeze over but the bigger lakes still have water. I doubt crampons would be of much value until the snow is over 1 foot deep. You will need to be more careful going around areas that are frozen...like the Waterfall pitch below Iceberg lake and the chute above the notch. Also crossing the river between Lower and Upper Boy Scout lake can be touchy.
