There are two areas of concern. One, of minor concern, is the Grapevine, which is an area of I-5 south of Bakersfield and north of LA. It occasionally gets snow and closes. The reason not to worry too much is that 1) it happens rarely, and 2) there are routes around it.
The other area of concern is the Siskiyou pass on the Oregon/California border; and in general, the Siskiyou mountains between Ashland OR and Redding CA. The pass can close due to snow, and the entire area is subject to chain controls. This can happen anytime between Nov and April, though dead of winter is more common. It's a concern because if there's a big storm system hitting the area, it's likely that there will be no good alternate. While it's of some concern, I'd simply keep an eye on the weather for Northern CA and southern OR. You may have to change your plans by a couple days one way or the other, but you're not likely to get shut down for an entire week.
-Bob