I would reserve for the upcoming labor day weekend this September 4th, in advance wherever your at! Most locals go camping on that end of summer weekend from my experience! John
Another thing to remember is there are CG's in the upper mountain regions that may close during the winter months due to snow including the grapevine that connects northern cal to southern cal. The best thing is to keep abreast of weather conditions in the areas you want to travel to ensure not getting caught somewhere you don't want to be! Sorry if that sounds ominous - but if you're used to all kinds of winter driving - then go for it! A word of caution - since we've had all these fires this year, a lot of areas may have flash flooding once we do get rain. If you're prepared, you should enjoy our state!
Remember, the first day of Winter is December 22nd this year. I have found after New Years Day that it is really easy to get in most places anywhere in California...perhaps more difficult in the Palm Springs area due to snowbirds, but still possible nevertheless.