I have not heard that mentioned in a long time. Where i teach art in elementary and kindergarten, kids used to say this all the time. But it has been a few years since i have heard any kid mention this.
We used to occasionally do this in school, and it led to massive confusion. If I remember correctly we agreed on turning words into their opposite but not negating at the same time (like with "not"). Alternatively you could negate a sentence without changing the actual words. This way we had at least some pattern and it was somewhat possible to still have conversations on Opposite Day - even though it usually took the other one 2 minutes to process what you said and reply to it, and vice versa.
Either way (and here I go by the rules again XD) Opposite Day is mirthless because everything people say is so crystal clear.
I don’t think most people in America have heard of them either. I don’t know if it’s the same in England, but there are small holidays almost every day that most people don’t celebrate or know about.