Ffuser1 create a permission group called "Horse Riding Moderators", then in the permission grid assign the permissions that these moderators needs for the tag "Horse Riding". Now assign users to that group.
It's not as simple as defining the role Moderator and then selecting which users get that role for specific tags. Permissions are always complex and keeping them simple while versatile is a very tough job.
Let me know whether my suggestion suffices.