Ground person here, not pilot. Cat I, II or III relates to particular approaches, not to the airport, and is generally related to the ground equipment that is available/working. If the airport has a Cat II/III approach available and the weather drops below that where a Cat I approach is likely to be successfully completed, then the Cat II/III approach will be made available - this is usually notified by the phrase 'Low Visibility Procedures in force' on the ATIS. Nothing much changes as far as ground equipment is concerned (except that back-up generators are usually switched on and may become the primary source of power for some systems), but ground procedures will change to 'protect' the approach guidance signals from interference and to reduce the risk of ground collisions. LVPs will typically be introduced at an airport if the RVR falls below 550 metres or the cloud base is below 200 ft aal, but some airports will have different criteria and may introduce restrictions in phases/stages. In my experience (mainly around Europe), RVR controls whether an approach can be commenced and, sometimes, continued below 1000ft, but at DH the only thing that matters is whether the pilot has the required visual reference. However, if a plate says a particular minimum ceiling is required, then I guess that's the rule - the national authority has the ability to stipulate additional limitations or requirements if it is felt necessary. Don't know if that helps......