The natural world is just about the perfect setting for "The Snow Man," and that's not because snow men just look so much better against a backdrop of leafless birches and evergreen pines. It's because the natural world is supposed to be outside of the human world. It's not something we can change or control. It's Mother Nature. But in this poem, Stevens turns that notion on its head, and proves to us that the natural world is, like just about everything else, all a matter of perspective. We may think the world turns and the seasons change and there's nothing we can do about it, but Stevens begs to differ.
The natural world in this poem is entirely irrelevant. It's just a tool Stevens uses to talk about ideas.
The natural world is essential to this poem because Stevens is talking about the kind of philosophical experience you can only have in nature.