I know that I've read this in more than these books, but I'm going to write about Heidi by Johanna Spyri and The Secret Garden by Frances Hodgson Burnett.
I just think about these two books from time to time, sometimes when I've seen something awful from Bad Medical Takes on Twitter. We all have some crazy ideas about health. In each of these two books, a child who has needed a wheelchair to get around is cured mostly by spending more time outside. It's crazy.
I was fascinated with Heidi when I was a kid. This little girl is sent to live with her grandfather in the Alps. I had an illustrated version, and I really think it might have been A Little Golden Book. Anyway, the grass looks so soft, and the work that she and her little friend to with the goats doesn't look like work, and the goats are cute. Then, Heidi is sent away- and I can't remember the details- but it's something like being a companion to a little girl named Clara who isn't in good health. Naturally, they get Clara up to the mountains, and after awhile, she's out of her chair. She was outside and drank goat milk. Good for you, Clara. You can have my goat milk, too, because I'm not drinking that.
In The Secret Garden, it's a little more complicated- the condition that is keeping a little boy in a chair might be imaginary. His father has a crooked back (that's all the explanation there is), and with that and other reasons, the boy, Colin, is terrified of having a crooked back and not being able to walk. He has no strength except to have tantrums. So, Mary gets him out to the secret garden and he begins to get well. I'll admit that it isn't 100% the magic of being outside- he does exercises- but still.
Did the Victorians have the idea that outdoors in the country cures children's ailments because of all the coal dust in the cities? It makes me think of Elizabeth Gaskell's North and South- there's so much cotton fluff in the air where people are working that it makes people sick. If only those kids could've been out of doors. (And in my country in the year 2023, regulations against child labor are being taken down, and we're finding out that there was more illegal child labor going on than we had any idea of.)
I'd like to see any other titles with this trope- I know that I've read it elsewhere. I have to say, I do think that there's something worthwhile to getting outside, and for kids to be able to play outside. It's only the idea of it being a cure-all that I am poking fun at.