In my limited bike experience in really thick fog, I agree with sudo bike: too much headlight can just blind you. It bounces back off the white in front of you. I've got a good bunch of boat experience that echoes this. I have ridden on a MUP in that kind of thick fog, and would continue to do so though I'm very concerned the whole time I'm doing it about a head on with an idiot going too fast. You basically have to navigate off the curb / trail edge and work with a VERY limited event horizon. I don't think I'd be on the road with cars in pea soup.

With fog that you can get a bit more visibility in and make out objects a bit further out to 20-50+yds, I agree with the trend of the posts towards reflectors and blinkies mattering a lot.