Yes, we can land in fog, provided that (There's always the small print, isn't there?) :
1. The pilots hold an Instrument Rating (IR)
2. The Ground equipment is suitable, e.g: Instrument Landing System (ILS)
3. The aircraft is ILS equipped.
Category 1. For a manual or automatic landing we require a Runway Visual Range (RVR) - that's visibility along the runway - of 550 metres and must see the touchdown area by a Decision Height of 200 feet.
To go below that we must have autoland fitted.
Cat 2. RVR 350m DH 100ft
Cat 3a. RVR 200m DH 50ft
Cat 3b. RVR 125m DH 15ft
Cat 3c. RVR 75m No DH (As long as the equipment monitors do not pick up a defect we let the aircraft land.)
Military pilots are no better trained for low visibility landing than civil (except for special ops using vision enhancing devices)
We don't avoid landing in fog for safety reasons - with the right kit and training for both pilots and air traffic controllers it's very safe - it's the taxying around in 75m that's difficult
Yes, from the foregoing you can see that limits vary according to the level of equipment fitted at the airport and on the aircraft; also if, for instance, any one pilot or flight engineer has not yet completed the low vis ops part of his training on type then the whole crew/aircraft/airport combination will be limited to Cat 1. Undulating terrain close to the approach end of the runway may also affect limits. Some airports have an artificial 'radar floor' of reflectors to give the Radio Altimeter an accurate datum.
Pedant notes
Some airlines have had Cat 2 manual landing using Head Up Displays (HUD).
There may be slight variations to the above figures from airport to airport.
So, what happened to the FR421 STN-PIK last night???
