The speaker dresses in mourning and walks into the woods, as if heading to a funeral. We never learn who or what is being grieved, and that silence makes the grief feel private and heavy. Once among the trees, the wind drops, and the speaker stays until late. Then it rains, and the poem tells us the rain is sad.
The title is the key. "Pathetic fallacy" is the term for giving human feelings to nature, so that a storm seems angry or rain seems to weep. The poem sets up that idea and then plays with it. Does the wood really respond to the speaker's sorrow, or is the speaker just seeing grief everywhere? The word "sadly" could be the speaker's own mood projected onto the weather.
The mood is quiet, still, and lonely. The short lines and plain words leave room for silence, and the wind falling feels like the world holding its breath before the rain.