Once the facade of civilization is lifted and the utilities collapse, then the most common weather changes, seasonal or otherwise, will result in shock and awe to the survivors. If you have a roof that's leaking in heavy rain or no utilities to make your house warm in winter, then you know just what I mean.
Winter was a very cruel punishing time in history. From the harvest to the earliest re-gathering of wild edibles and farming, there's a period of about eight months. While some things are to be found in Nature, they're not in an abundance, and so you have a lengthy period of possible starvation unless you prepare. This meant not only harvesting, but gathering enough in your storehouse to have adequate calories for that long cold period. No one could possibly store enough, and weight loss was an regular part of this cycle. Death too for the weakened members of the tribe.
With the cold and exposure, there naturally came sickness and death as well. Unless you have a way of insulating the home, alternative heat sources, readily available fuel and seasoned wood, then you'll freeze to death.
In Winter there is far less rain. If rainwater is your planned water source, then I've got bad news for you. You'll be praying for rain, that's for sure. When it comes in the Autumn and Spring, and there's no sewage system, or failing drainage, then it can ruin crops. Too much rain will result in high mosquito populations and sickness. If it doesn't come in abundance, then the drought will kill plants. You're entirely at the mercy of rain unless you create a reservoir of water to irrigate the plants when you decide they need it, not when Nature desires to rain.
The temperature will determine the length of a harvest. If it gets too warm, then many vegetables bolt and turn to seed. If it isn't warm enough, then seeds won't germinate. If the season is reduced by cold weather, then some food won't be harvested but die to frost or simply not get far enough along to ripen or fruit.
Hail can suddenly appear and damage fragile plants. This means having a way to temporarily cover the garden with tarps might protect it somewhat, but realize that your garden in a collapse will be far LARGER than you might expect in order to realistically feed your family or community.
Winds can easily destroy plants and infrastructure. A large tree falling is extremely difficult to cut without power tools and is a community activity since it provides many people with lumber or firewood. Imagine post-collapse trying to repair a home that's had a tree fall on it.
Weather now is a spectacle for most of us. It was a fearsome aspect of pioneer and tribal living. It will be again in the future if there's a collapse of society.