I have no first hand knowledge on Mosquito Flats, but you should have no problem at Horseshoe Meadow. There are actually 3 campground area at Horseshoe Meadow so if your preferred campground is full, there are 2 others. I've never seen it full, and I was there on Labor Day weekend a couple of years ago.
Wazzu, is there a map/website showing where all of the different campgounds are?