It depends on conditions and if the 4WD has snow tires.
http://www.dot.ca.gov/dist3/departments/mtce/controlmp.htm
Chain Requirement Levels and Traffic Control Definitions
R-1:
Chains, traction devices or snow tires are required on the drive axle of all vehicles except four-wheel/all-wheel drive vehicles.
R-2:
Chains or traction devices are required on all vehicles except four-wheel/all-wheel drive vehicles with snow-tread tires on all four-wheels. NOTE: four-wheel/all-wheel drive vehicles must carry traction devices in chain control areas.
R-3:
Chains required - Chains or traction devices are required on all vehicles, no exceptions.
R-1 and R-2 are the most common chain controls. The highway will often be closed before an R-3 control is imposed.
C
Road Closed
S
Split Control - Chains or snow tread tire requirements are set at two separate points of the highway for different requirements. It is not uncommon to have R-1 conditions from point A to point B and R-2 conditions from point B to point C.
T
Truck Hold - During major storms when traffic flow is heavy, Caltrans may hold commercial tractor-trailer combinations at specific points below the snow line. These points typically are:
Eastbound I-80 at Applegate (east of Auburn, CA)
Westbound I-80 at Verdi, Nevada (west of Reno, NV)
H
Hold Traffic - Traffic is held due to spin outs and accidents. When the spinout or accident is cleared, traffic is then released.
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