From my experience with the Closed Beta i don't think i have encountered a fog or mist, currently there's haze but i think that's the game draw distance being rendered where you see the silhouette of the ships in the far distance.
Currently as the weather changes from time to time, introducing this feature to the current weather cycle, as in the real world mist/fog usually appears in the mornings, I believe the introduction of fog and mist would have a big impact in the game as this would allow for treasure hunters a opportunity to gather up some treasures and would imply a more defined communication with your crew as you would barely see the island until you are almost on top of it, also would be a challenge with the pirates that want to take you down.
Imagine sailing in the dense fog as you wouldn't expect to be alone and all of a sudden a big galleon appears within the fog to ram your ship! That is my vision and the immersion you would get with this feature!
Something like this: https://imgur.com/f7A4lz5
Let me know what you think, the possibilities are endless. ps: Sorry for my bad english and sorry if this as already been mentioned! ;)
Edit: I have created this two images from ingame screenshots to better illustrate how mist and fog could work ingame.
