Precautions when riding in long-term low visibility Heavy fog or a narrow, overgrown and winding trail, can reduce visibility to 3 meters. Those conditions can continue for hours, and the safest approach 'don't go' cannot be always taken.

I find that riding with appropriate speed as to be able to stop within those 3 meters can be quite fun and rewarding riding experience. This allows for safely intercepting tourists and animals (boars, turtles, bears, cows, horses).

However, should a runner or another cyclist approach from the opposite  direction, being able to stop by the end of your vision field becomes insufficient to avoid a crash. What steps can be taken to reduce the ever present risk of this happening. 

One approach is riding at walking pace or just walking. This seems appropriate to city parks or heavily inhabited trails. However, on a winding trail, this could mean pushing the bike for hours. Clearly not mountain biking!

I have used a small speaker with quiet popular rock music. No idea if it did increase safety, but it did annoy some tourists, wanting to enjoy nature and peace.

The only bike-only trails in my country are several downhill racing courses. All other trails are shared, with widely varying traffic loads.

I have trails like this in mind, but with more vegetation and more turns:
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).