Is probably from the USA.
You say this as if you were British, but then the rest of your comment seems to suggest that you're not (in which case it's not surprising that you might be unaware of some aspects of British playground culture).
It is a part of our culture, like pubs, pooh sticks, morriss dancing or cheese rolling.
It would be a totally valid citizenship question.
Maybe you're a city child?
It certainly is a mainstay. A yearly treat which children love. In Ireland I was taught this song in school: https://m.youtube.com/watch?v=bhebvq0O4GY (and I still remember all the words)
For sure it is. Every boy (and probably some girls, but never seen myself) plays conkers and likely puts their life in great peril climbing horse chestnut trees to gather the best conkers before anyone else gets them.
When I think back now to some of the massive (old) trees I used to climb and the action of shaking the branches to try to get the chestnuts to drop (whilst the branch is breaking underneath you, 100ft up), I’m surprised I’m here to talk about it!
This is a serious business.
A horse chestnut tree can reach heights of approximately 30 to 40 meters (about 98 to 131 feet) [1].
I used to go pretty damn far up, one time really shitting myself up as the thinner weaker branches started breaking away as I was climbing higher.
It genuinely felt like, even if probably not entirely true, that I was sticking my head out of the top of the tree before it started giving way. It’s a memory that will stick with me forever!
Of course I can’t prove this, but it’s not entirely implausible that a very old horse chestnut tree could be over 100 feet high and it’s not entirely implausible that it’s possible to climb up a tree of that size. So I guess either take my word for it or not, your call ;)
[1] https://directree.org/horse-chestnut-aesculus-hippocastanum/
It's a load of different morriss dancing troops dancing around the town with a parade with the lot of them. And there are a lot. Bloody freezing some years though!
Also, in the same vein, this weekend I think there's the annual Sea Shanty festival in my home town.
https://harwichshantyfestival.co.uk/
The videos are quite bad at conveying how great some of the groups are, especially sitting in a smallish pub with a pint listening to some amazing singers do sea shanties. Quite magical.