[X] Head into the fog, Sharingan out, fists of fury ready to punch anything that might be in there. Can't be that bad, right? Maybe you'll fulfill your good deed quota for the week too.
[X] Rapid exfiltration out of there, avoid Hiding Like a Mole. Consider explosive demolition-into a dynamic exit- if necessary. Fog and monstrous shrieking noises? No thanks. Meet up with Sugiyama ASAP. What the hell is up with this?
[X] Foggy weather? Loud noises? Sounds like "cover"! Use this opportunity to go find more intel about the local ninja clans. Go investigate all of those temples.