It should also be mentioned that the weather forecasts in TS3 must be some kind of joke. They are only typically accurate in some kind of random sense, such as a broken wall clock that is correct exactly twice per day. Every mod developer who has been asked to improve upon these has looked at the code and said something like "Not in our lifetime!" I've always taken that to mean that the game's weather patterns do not set themselves up in advance and are thus just not able to be predicted as they might be in a world where weather events form and move towards or away from us in relatively easy to see patterns. The best that any kind of forecast would be able to do is base things on what usually happens in that world in that season, with or without mods to favor some weather events over others and adjust temperature extremes, not on weather events that may be "on the way."
If you want less than sunny weather, schedule a massively huge life-event celebrating party outdoors with no viable indoor backup plans in place. I guarantee you that the raindrops will start falling as soon as the first guests arrive. :p
There's always the NRaas Tempest mod to establish and fine tune climates per world. But for a more immediate effect, one can use testingcheatsenabled true and shift-click on the ground to set the current weather conditions (and in some cases save your outdoor party that was planned so carefully from becoming a soggy mess).