Seeing Marcopolo's picture reminded me of how beautiful Joshua Tree is.
We were there a little earlier, the first week of February, and stayed 3 days. The main CG's were full of the big RV's but there was plenty of room at "White Tank" (a "B" size campground).
Make sure you are full when you go, there is nothing out there(including water) except peace and quiet and great scenery.