There can be some significant crosswinds in Cat 2, but wind strength generally decreases in thicker fog (Cat3). However, some auto land systems might have to cope with blowing snow or dust which could result in ‘Cat 3’ visibilities.
Auto pilot certification has to meet stringent requirements (JAR-AWO) to achieve a reliable touch down in an acceptable landing box. Some of the data originates from flight testing, but most is provided by simulation of the autopilot performance in a wide range of variables, which are based on the flight tests.
I flew a 35 kt crosswind auto land to certificate an AFM limit of 15kts. The auto land appeared to be very capable, if not more than I could achieve in the conditions. In my experience the auto land limits are conservative, rightly so for systems where human intervention is either not required (Cat3b), or not guaranteed.