Never having read that book, nor for that matter seen any version of the film, I can't answer directly.
However, from my own experience, nature, in the form of open land with possibilities, gives children an area in which they can play, take risks, have an adventure, learn, make friends and be themselves without adult supervision.
There was an interesting programme on Radio 4 yesterday about adventure playgrounds ... you can listen to it here and it might give you some ideas.
Huderon - you took the words right off my keyboard!
Children in previous generations (including mine!) hads far more freedom to roam than they enjoy today. The outside world was full of possibilities, and freedom to immagine and play without adults being around. It's natural therefore that they would empathise with children in fiction doing the same thing.