I see now that something similar is being done in Belgium. Except of course that in Denmark the camp_site would not just be a small zone / area but often an entire forest. Does that make it different?

WikiProject Belgium/Bivakzones - OpenStreetMap Wiki

To complicate the matter there are also several free, basic camp sites and shelters on both public and private property in Denmark. These are already added to OSM but as nodes since these sites normally dont include the surrounding area or only a very small part.