You can get almost real-time temperature and snow (actually water content) from a sensor near Camp Keola at Huntington Lake:
Also take a look at the Sierra Summit cam. One of the usual views is of the lake. Or, look at a webcam at Shaver Lake.
Or check Sierra Summit's current snow conditions.
A few miles south is the Sequoia-Kings Canyon National Park webcam, and the Hume Lake cams.