The table in the guide under the heading: Weather By World List is what the code shows as typical seasonal weather for that particular world. So each world has coded 'base weather'; for example it can snow in Oasis Springs very rarely but it will not settle compared to it will snow in Willow Creek often and settle.
That is quite different to weather forecasts which predict the weather type for that particular day in that particular world. You'll notice that the weather forecast changes as your sim travels to different worlds on a same day, showing that weather will change form world to world but the Season will remain constant.
You can also see the actual weather and the weather forecast without opening the calendar buy hovering your mouse over the weather icons next to the time in-game at the bottom of your screen.
So for example my sims are at Granite Falls: the forecast says 'Snow' and the current weather is 'Windy and Freezing'. This is how the game should work. Forecast is a generalization of the weather to expect on any particular day, the Current Weather is what weather is playing out in your sims lot at this moment.
