Any highway licensed vehicle in CA can operate in any public area open for motor vehicle use.
Current OHV law in CA reads;
What is an Off-Highway Vehicle (OHV)?
Any motor vehicle operated off-highway is an OHV. A highway licensed vehicle is an OHV when operated off of the highway. Vehicles having Green and Red Stickers are OHVs. Some of the more common OHVs include all terrain vehicles (ATVs), dirt bikes, sand rails, recreation utility vehicles (RUVs), golf carts, snowmobiles, go carts, jeeps, recreational off-highway vehicles (ROVs) and 4x4s.
Does my OHV need to be registered (identified)?
If you are operating it on lands open and accessible to the public for OHV recreation, whether public or privately owned, it must have either a highway license or an OHV identification sticker issued by DMV. OHV stickers include "Green Stickers," "Red Stickers," and California Nonresident OHV Use Permits. See “C” below for Non-resident Permit information. The terms "registration" and "identification" are interchangeable.