Many publications have been dedicated to predator and prey activity respective to moonlight conditions.
Some species adjust their behaviour in accordance with the brightness of the moonlight (when accounted for cloudiness or the habitat type, e.g., dense forest vs. open field vs. rugged terrain etc.).
Others (or in other circumstance) do not seem to take great notice of moonlight.
However, I have not found any publications discussing the effects of fogginess on predator-prey dynamics.
This would be an interesting topic to address both from the perspective of general fogginess (periods when extensive and thick fog cover is observed over vast areas) and from the perspective of foggier times and places (e.g., the use by species of riparian habitats vs. habitats further from rivers or adjacent forest/meadow patches where the meadows accumulate mist but the forest does not during the same morning hours).
There might be other perspectives that I have not currently considered but these two come to mind first.
Notes by Ieva 