I've been taking my LA based Scout Troop to Sequoia every year for this. We snowshoe to Panther Gap. It's pretty reliable. We've tried the San Gabriels, San Jacinto, and Mt Pinos but the conditions are too unreliable for long term planning. This year we plan to go to Yosemite and hike out of Badger Pass.
We backpack in using REI 4-season tents, then build snow shelters as an option. We build a large communal kitchen where we spend most of our time. Dig and sculpt it then put a tarp over the top.
Buckhorn Campground in the San Gabriels gets great conditions at least once a year but that area is always technically closed. You need to watch the weather and get up there right after a big storm.
San Jacinto can be pretty good. LAAC runs winter camping training out of there using the tram to get up to the snow.
For this year, if you don't want to drive to Sequoia, you should go for the San Bernardinos.
There are not many places where you can just car camp and do this so I advise backpacking in. This is for older kids. The 11-12 year olds cannot restrain themselves from getting soaking wet within 2 hours of arriving at the snow.
LAAC opens Forest Lawn Scout Reservation at Lake Arrowhead in the winter. www.boyscoutsla.org