Snow is the greatest danger for hikers, especially California hikers who have little experience with winter conditions. Not only does one have to contend with cold, wetness, and wind, but sometimes trails get obliterated. I and a friend were caught by an overnight snow storm on southeast Shasta and we spent several hours looking for the trail.
Weather changes rapidly at high altitudes and gets worse with altitude.
If your group includes inexperienced and weak hikers, I would definitely turn around. It's difficult to get lost on the Whitney trail, but it can get real cold.