Yes there are tons of "trails"! Well, technically roads... but when they arnt plowed, they might as well be. Stockish can have pleanty of fun on any un plowed road. If you are locked or have chains, you could do alot more.
It depends on where you are planning to go. Generally around Shaver Lk area you have to carry chains with you even if you have 4wd and snow tires. It sounds like everywhere else in CA is a lot more relaxed.