Current forecasts are for up to 2 feet of new snow above 7000' in Charleston area. It will be soft powder, unconsolidated. Shorter climbs -- e.g North Sister from the N side, Fletcher from the back, Amargosa Overlook -- may be reasonable with snowshoes, but there could be big sloughs.
I've done Griffith with snowshoes in soft powder twice (6' snow) -- just start early.