The point people don't seem to get, why is a mystery, is that closure and openness have nothing to do with facilities. It's to do with what the owner of the field has decided. Thus a major airport with facilities to cope with airliners might be closed to all traffic for some reason and a farm strip with no facilities at all might open to all comers.
It then behoves us as pilots to find out about and respect the wishes of the owner, apart from some legal implications in some cases, it's just good manners
Licensing is an entirely different matter and the need for a licensed aerodrome is covered by the aircraft operator's activities. Most activities including training, involving a light aircraft do not require a licensed aerodrome, certain commercial activities would need such an aerodrome, but this forum is about private flying.