Weather was quite important for colonial people and adding a weather mechanic to the game could do several things. First it would simply add visual variety to any outdoor environment, second it could add some semi-randomization to any crafting process that take long periods of time, third it could create variation in the availability of many goods over space and time thus encouraging trade between players.
Types of weather would be fairly simple, sunny, rainy, cloudy, windy, stormy. Sunny looks like current Salem, cloudy could look and even act as mild darkness, rain is also dark and adds some 2D rain graphics in front of the camera, windy has some air-stream wiff animation also 2D and stormy is just rain and wind together both visually and in it's effect.
Each say 6-24 hours the weather changes for everyone but it dose so in a non-uniform way using perlin noise to create 'blobs' of weather that are comparable in size to existing biomes, the blobs might shift each time weather changes by use of 3D perlin noise, the granularity of weather might be very low say the size of a mini-map if it is found to be necessary to keep computations reasonable or the player finds that more manageable, but like animals weather doesn't need to exist until the player is present and any player made crafting that needs to be weather sensitive can just check very infrequently so I don't foresee much of a problem.
While all players can just see the current weather in their current location they can also use an adventure option to predict weather for their location (and maybe some surrounding locations) several cycles into the future, the prediction accuracy is determined by Frontier&Wilderness proficiency but in all cases gets less accurate in the future. The prediction is done deterministically using perlin noise and the players proficiency level so spamming it produces the same result, only a higher proficiency will yield a better result. Predicting the weather costs nothing but a little time.
Agriculture is the most obvious thing to be effected by weather, each type of weather could simply add or subtract from the 4 influences or add or subtract Upkeep, Plenty, Speed and Influence just like fertilizer. This might be good or bad depending on what the farmer wanted to raise/lower so planning around weather is important. This element of randomness will make high tier crops a bit more luck based as you will need to hit a streak of idea weather to grow them.
Foraging could also be significantly effected by weather, certain foragables only occur in certain weather, or in the case of mushrooms AFTER a certain weather (rain), the relationship can be a combination of biome and weather as well, say for example tumble weed always occurs in desert, but occurs in other terrain only during wind. Foragers who know their weather relationships and who watch and plan can more effectively find what they want.
The drying process of boards with it's rather crazy space requirement could be replaced with weather effects, the more rain and clouds the more moldy boards. Other crafting processes have potential to be simply made faster or slower, drying racks, baking tables, smokers, possibilities are nearly endless for smart players to increase efficiency by monitoring weather and adjusting when they do certain things, ideally every profession would be effected in some way but would never be shut out entirely from doing something useful.