How odd. We went a couple of years ago - drove down on Jan 1, in the park the 2nd - 5th, and it was great! It rained at little one day, but being from a wet winter weather area, rain was tolerable for us. I did find that qestionable weather keeps many of the locals at home (our sis & bro in-law live 20 minutes from the parks, and clouds keep them at home).
I think the post new year's crowd depends on when during the week the holiday falls. When the 1st is mid-week, many get the week off (or long weekend before). I think I would risk it and go. Be prepared for cooler weather, and try it. It still won't be as bad as summer (or the day after Thanksgiving, or Veteran's Day, or New Year's Eve & Day).
Also, my youngest 2 start back to school on Jan. 3rd, so at least most of the crowd from our area of No. CA would be back at home.

I just noticed we are from the same area. The middle and HS students go back on the 7th, but the year round start back on the 3rd.