Precautions when riding in long-term low visibility
Adjust your speed for the road/trail conditions, especially on shared trails; they are not meant for "high" speed cycling.

Anecdotal, in Montreal, on the mountain, there's a gravel path, the Chemin Olmstead, shared by everyone, walkers, runners, cyclists and families, when cycling, it is understood that we should go slow, going and more especially going down.

If the trail is not large enough and you are forced to dismount and walk, then you should not bike on it.

In the fog (and night), you need to make yourself visible, wear some reflective clothing/harness/sash and have some small blinking lights in front and back of your bike (blinking is better than always on lights)

As for the music, I would advise against it, it is annoying as heck and it not a safety plus (IMO).