There are two independent camp-grounds in the Horseshoe Meadows valley.
1. Cottonwood Lakes TH CG
2. Horseshoe Meadows CG
In my experience their popularity corresponds to the above sequence. I have never seen both of them filled, and though popular, the Horseshoe Meadows area still remains over-shadowed by such trail head campgrounds as Whitney Portal and Onion Valley, and unlike Onion Valley the Horseshoe Meadows Valley has two campgrounds. I think you will be fine, you may need to bounce around a little, but you should be fine.
Actually, there are 3. Add the equestrian.
