No need for chains for the tires. Once installed, you can only drive 20-30 mph (30-50 km/h), and with a tight driving schedule, it's probably better just to cancel that portion of the trip instead of driving there slow.

Mountain highway passes in Southern California are most likely either closed or open, instead of requiring chains like in Northern California and in Southern California's ski resorts. When they clear the snow, they'll reopen the road.