I have little experience riding in really dense fog, but in addition to all the comments about lighting I would add a rearview mirror might be a last line of defense against the sudden appearance of an oncoming car. I would probably check the rearview quite frequently. Also I would turn my radio or I-pod down really low, if not off.

I would also be on high alert for something oncoming, or in the road ahead. Naturally (for me) I would be riding slower.