Certainly depends on the aircraft type and the specific operator.
Example.
With some L1011 operators (but certainly not all, in the past) autolands to CATIII standard were fully approved on contaminated runways (wet, but not icy, snow OK) with crosswind limitations (15 knots), and full rollout guideance was always available.
Derated and flex takeoffs were also permitted on wet runways, provided anti-skid was fully functional.