Yes on all the above tips on driving south.
Cari & I have taken our van down from Northern Oregon via i5 through the passes on the Oregon/California boarder, and then the one mentioned toward LA (the "
Grape Vine"). We've taken trips in January through May. We've had a hit-miss with snow in the passes off-the-roadway and were able to time things to be able to drive through with the truck traffic. Once, upon arriving in Sacramento we saw that the Or/Ca pass had closed down a few hours after we got through. You just never really know...and that was a trip in late April !
Now that said? My advice is be a bit flexible. The main areas you might have issue are already mentioned in the prior posts. What you could do is have a back up plan in say the Eugene - Corvallis Oregon area (Before you head into the Medford/Grants Pass Oregon area and the boarder-hills/pass). Then look into possible overnight opportunities in the Stockton/Tracy California area which is before heading into the hills on i5 heading south toward the Grape Vine.
Oh one other area that was crazy for us one trip down... we actually got trapped south of "Weed" in Northern California...due to heavy rains and flooding on i5 that closed the highway for several days. Freaky and unlikely, but still possible. We had some extra time in our vacation and just spent a couple extra days in Sacramento with family waiting for the road to clear. Sure we could have spent an extra 6 hours on the road and gone north on i80 over Donner Pass to Reno then north on 395, but it would have required chaining up for any non-AWD rigs (we had a volvo xc wagon so could have done it...but...i really don't like dealing w/Donner and snow. Thoughts of Cannibalism come to mind
Have fun on your adventure!
Thom