Each biome has its own set of changing weather patterns. You can get a general idea of the weather when you're choosing the map to play. Temperate weather/climate is the easiest. On top of that, naturally the weather won't be exactly the same each and every year. One year may be easier than another, perhaps colder year.
Seasons, weather & production
The weather in Patron is important for multiple reasons, both in visuals and as a gameplay element. As the seasons change, so do the weather patters, air temperatures and with that some buildings can be affected efficiency-wise. For example, the Gatherer's hut, although it has no standard upkeep to pay other than actual workers assigned to the job, will have drastically lower production output in the cold Winter months. Similarly, a field, even when placed on very fertile ground can yield much less produce if it suffered a heatwave or an out-of-the-ordinary freak cold front. The city you build in Patron is not some laboratory-study. It lives and breathes with the environment and if that is experiencing some drastic changes, it will reflect on your city. And not just on production.
Impact on health
Your citizens can get sick. More so in bad weather. During Autumn and Winter you can easily expect your people to spend more Herbs and Medicines to stay healthy or at least to fight off the onset of a disease. Similarly, more drastic weather will have a stronger impact on health.
Weather and disasters
Some natural disasters, like a cold front, heatwave, raging fire or a disease outbreak are also affected by the weather. Meaning, some are more likely to occur in certain weather conditions. You can easily expect an especially cold front during the Winter, or a heatwave in the Summer. Vice-versa not so much.