you should never pay to camp around mammoth. You can drive out the scenic loop and camp anywhere 100 feet off the road. There are at least 50 "camp spots" all ready established. Just stop by the forest service and get a fire permit for free. If the scenic loop is too cold you can drive out of town under the 395 overpass and camp off the dirt road by the power plant. Or out by the hot springs.
I talked to an Inyo forest ranger and he said Bald Mtn lookout or Smokey Bear Flats is the best place to camp this time of year. he also said you have to be 2 miles off the road for dispersed camping. A couple of us are heading that way next week from Ohio. Hopefully there is plenty of dry land as we plan on camping as well.
There are some spots with trees depending on where you camp, but it does get windy in the afternoon / evening at times.
If you leave your tents out make sure you put in some heavy rocks or something. We've come back to our spot one time with our tents blown 50 yds or so through the sage, with all our camping gear in it.