Our house doesn't really change much in decor, the blankets get used more sure, and we use incense, essential oil burner and such like when we feel like.
What does change, subtly at first, is how we eat, what we read, how we watch tv. In the autumn we watch more films because you are "settled in for the evening" earlier. Read books which have autumnal/winter settings. Play family board and card games that last a bit longer and are slower in pace.
But it's mostly with food that we see the seasonal changes.
Main dishes that take longer to cook, but more hands off, things stewed in the oven, hot desserts, baked apples are amazing. Even just warm milk on the muesli in the mornings. Herbal teas instead of water in the day.
So it's a subtle shift that is in reaction to the temperature and weather outside.
We have BBQs in the autumn, not summer it's too hot to spark up more heat, but as the temperature drops, around 18C mark then we start cooking on fire outside and sitting around the fire pit, we have a tripod and make mulled cider and such like out there. But that is how we use our garden fire to keep us outside more when it's cold not in the summer.
It's almost like in summer everyone is doing their own thing, going out, kicking balls around, and in autumn we come together a bit more around the fire or table, even the music we listen to changes. And I am more prone to read "a poem a day" in the autumn, where we critique it as a family! Although there has been much of that recently remembering the genius of Tom Lehrer, who was basically the motto writer of our children's childhood (obviously we had to move through his body of work like how you move through the film age ratings).
So I would advise to not to overthink it too much OP and go with the flow and temperature outside. For us seasons aren't really something to go out and design and tick off a list, they are changes in states of mind and activity. If you want the practical side, I get out the winter footwear, check it still fits, is waterproof and if not make sure everyone has a pair of decent walking boots, wellies and weatherproof trainers and school shoes. Again with the winter and weatherproof/winter coats, hats, gloves, scarves and make sure that there is still a set of thermals which still fit and for the teens sports thermals (including gloves) and that their bicycle lights still work and are charged etc. Keep a winter medicine cabinet up to date and towards deep dark winter, with the potential of bad snow/ice, have a stocked freezer/tins in case of anything unpredicted, like nothing over the top, a week maximum, not even that.