The thing to watch with lights in fog is that many lights shine light sideways and upwards as well as forwards.
Normally, this is great for making you visible from the side. But any upwards-shining light will light up the fog in front of your face, making it harder for you to see through it.
Fortunately, this is usually easy to fix with a judiciously applied bit of black insulting tape.
I was out yesterday - foggy in the morning, but it cleared up and was beautiful in the afternoon. Then freezing fog as it got dark again. On the last bit getting home, I met the local roadie club coming the other way. Those guys had some seriously bright lights!
The frontal surfaces of me and the bike were covered in a thin layer of ice when I got home!