At any one moment you can see one of six types of weather outside.
Clear (with a few puffy clouds in the sky during the day, or stars in the sky at night), overcast, raining, lightning, typhoon (strong blowing wind), or snowing.
The weather may change up to 5 times a day. (I'm not sure what times of day it changes.)
Each day's weather pattern is determined in advance. (I assume this happens when your TMGC+C character wakes in the morning.) If you visit the playground between 7:00 AM - 9:59 AM, you may see Guidetchi, who will tell you what the day's weather will be. (Unfortunately, you have to be able to read Japanese in order to understand what he says.)
Example weather patterns:
(1) Snowing all day and night.
(2) Rain at first, then cloudy, becoming clear after noon.
There are six weather patterns possible within each month. There are 20 weather patterns possible throughout the year. The six possible within each month depend on the season.
The conditions you see outside depend not only on the weather, but also on the time of day. The overall lighting changes for dawn, daytime, dusk, and nighttime.