The cloud symbol doesn't indicate fog, just that it would be cloudy. Trying to remember but I believe the way the game describes it is that fog appears after a spell of rainy weather. If you see 3 umbrella icons on the weather forecast then I would take the last day as the deadline. Therefore from the example above, I would take the afternoon of Sat 16th to be the final deadline for you to clear that dungeon. It's no biggie even if you do miss it, the game just resets you back a week, giving you enough time to go through the dungeon, although I imagine doing S.Links again would be a hassle.