I think this depends on the company and aircraft-fleet!
At our company only Innsbruck is a captains-place, and we don't have any limitations for F/O-landings in Salzburg nor in crosswind-conditions!
Low-vis landings are capt. landings. CATII is flown as a monitored approch by the F/O and the CMD will take controls at the minimum if he has visual contact and do the landing, and CATIII is flown by the CMD with HGS!