The best way for children to learn about the passing seasons is to spend time outdoors... often.
Find a place (or a few places) that you like and are easy for you to get to. Try scheduling a regular time each week when you can go there, perhaps after school or on the weekend. In Britain many "country parks" are managed by the local councils and free to park and enter, but you could also try forestry commission sites, or invest in membership of the RSPB, the National Trust or English Heritage, Cadw or Historic Scotland if they have a suitable location near to you.
Just roam. Follow a marked trail or follow your nose (or the dog). Play hide and seek among the trees. Take a wildlife identification book or card, maybe birds one week, wild flowers the next, and trees the next. See what you can spot and identify. Go on a wild-food foraging expedition. Make sure that you're all suitably dressed and go throughout the year, whatever the weather. Watch the changing seasons and how the place changes. Take photos, collect twigs and acorns, blackberries and feathers.
We've recently moved to Herefordshire, and have discovered Queenswood Country Park. It's just a mile or so from C's new school, and while not strictly on our way home, it's only a minor detour. It's 123 acres, of which 47 acres are an arboretum with over 1200 rare and exotic trees. There are three way-marked trails, all under three miles, so more than suitable for little explorers, who delight in following the trail marker posts. It also includes a National Trust shop, free parking, a cafe and ice-cream shop (just for treats, not every visit!) and a brilliant adventure playground.
C has Forest School at school every Monday afternoon starting next week, so will already be suitably dressed for whatever the weather can throw at us, so I think we'll aim for a Monday after-school trip to Queenswood each week (with a flask of hot chocolate for cold days). Today they played for half an hour, and then we followed the Badger Trail for forty minutes. I asked them to look out for signs that Autumn is coming, and they obliged me with oak leaves turning brown, blackberries and beech mast. And the waggy-tailed-one wishes she could learn to climb trees so that she can better chase those squirrels!
I also love some of the seasons activities and printables that you can find on Enchanted Learning.
How do you engage with the changing seasons where you live?