Hi Greg,
Very few are closed, here's a good resource, although I wasn't able to find much re. seasonal closures, just info on dog restrictions.
A couple that come to mind because of Bighorn (lambing & watering times & areas), are Magnesia Falls at the top of Rancho Mirage cove, and the Skyline at certain times of year, (I think maybe Jan 15- June).
Here's the BLM site:
http://www.blm.gov/ca/st/en/fo/palmspri ... eadsb.html
Happy hiking,
ss