Winter in the Pacific Northwest has given me ample opportunity to observe the effects of rain and humidity on the visibility of distant objects. On a rainy day, even when it isn't actively raining, I can see buildings and bridges that are 3-4 miles away, and usually tall buildings that are 5-6 miles away, but seeing the mountains 40-50 miles away is not happening. When it is actively raining, buildings two miles away are often obscured. The position of the sun behind the cloud layer is somewhat vague; likewise the moon. The stars are totally obscured.
I've been thinking about the mechanics for getting lost during wilderness adventures and how they're sort of shit. I think rain should play a big part of in-world explanations for why getting lost happens. Distant landmarks disappear, celestial navigation becomes difficult, it just makes sense. I think, if you're tracking the party on a six-mile hex map and determining what they can see, on a rainy day it would be reasonable to limit vision to just adjacent hexes. Then, due to vagueness of celestial navigation, when the party attempts to move in a particular direction on a rainy / heavily overcast day, they may err by one hex-side. During actual rain or stormy weather, restricting vision to only the current hex is probably reasonable, which is the point where you really start to run into likely errors if you try to travel. If you're treating things a little more abstractly, where you don't figure out exactly what other hexes your players can see, maybe rainy weather imposes a -4 to Navigation throws, and stormy weather imposes a -8.
The difficulty in telling north by the position of the sun might prompt players to ask "What about compasses?" Compasses don't appear on the mundane equipment lists in the SRDs for any of 3rd edition, 5th edition, Pathfinder, or ACKS. Historically, magnetic compasses were developed by the Chinese and were definitely used for navigation by around 1000AD, with the earliest documentation of the use of a compass by European sailors was in the 1200s and likewise first documented in the Muslim world in the 1200s. So probably not something you'd want in a game set in fantasy antiquity or the viking age, but might be reasonable for your average high medieval game or for Oriental Adventures. Certainly it's less anachronistic than the 1600s-era spyglass present on several of the mundane equipment tables.
There was an additional note in the History of the Compass wikipedia article that I found interesting:
While the practice from ancient times had been to curtail sea travel [on the Mediterranean] between October and April, due in part to the lack of dependable clear skies during the Mediterranean winter, the prolongation of the sailing season resulted in a gradual, but sustained increase in shipping movement; by around 1290 the sailing season could start in late January or February, and end in December.Which reinforces my belief that persistent overcast should induce a substantial navigation penalty - it was enough to prevent shipping for six months out of the year. Granted, the penalty on any one daily navigation roll doesn't need to be very large for the effects on a long sea voyage to add up.