Yes their is camping at White Sands first come first serve or reservation available and there was snow at cloudcroft at this time it's cold at night at both sites but you can't go wrong when you visit both.
If it were me, I would go to Cloudcroft to find a camping spot. At 9000 ft. Elevation, will be much cooler.
There are 10 primitive tent camping sites at the park itself. They are first come first serve. They are a fantastic way to see the sands though
Not sure, it would be best to contact the Visitor Center there.
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