I've tagged a few "wilderness_hut"s maintained by the local students' athletes association. Since these are not open to the general public (you need to be a member to use them), the "tourism" tag is not quite appropriate. Still, the tags commonly used together with the tourism tag fit well, so I've started putting tourism:private=wilderness_hut on them as a main tag. This maintains a relationship with the main tourism tag while preventing the huts to appear on tourist maps.

An alternative scheme would be to use tourism=wilderness_hut;access=private, but adding negative information in this way is generally frowned upon. It would require all users of the tourism tag to also check the private tag to find out whether the hut should be rendered.