California in winter is generally rainy, but otherwise not an issue. The I-80 - road from San Francisco to Tahoe - may be snowy after you pass Auburn - as others stated, the chains might be required (this happens relatively often), or it would be closed completely (this is rare for I-80). Highway 50 is an alternative road, but it is not suitable for RV in winter (one lane, windy), and is more likely to be closed. Don't drive to Tahoe from Bay Area on Fri afternoon, and don't drive from Tahoe to Bay Area on Sun afternoon unless you enjoy heavy traffic.
Your main problem however would be overnight RV parking. NateEldredge already mentioned difficulty in parking in San Francisco (to which I can only add difficulty of overall driving in San Francisco with RV). It will also be difficult in Mountain View - not as bad as SF, but we're getting there. Also driving through San Francisco Bay Area would be painful experience overall, unless you do it on a weekend, or late night/very early morning (4am) - we have very bad traffic here. Don't count on find a spot in the RV park in Bay Area - we have some, but they are occupied by people who live there for many years (rent here is crazy too).
Big Sur has day use parking (which also fills up fast on weekends), but if you intend to stay overnight there, you need to book a campsite. Those are usually booked well in advance (this is a very popular spot with locals, and there are few spots), so make sure you book one. If you don't, as far as I remember, there is no place to camp with RV overnight, it is pretty tight area.
No idea about Santa Barbara, unfortunately. Highway 1 will have no snow, but it has low speed limit (45 mostly), and it is quite windy itself.