The Speaker
We know little about the speaker of "The Woodspurge" beyond the fact that he is overcome by tremendous grief. This grief is never explained, and the only information we have about the speaker's life is that he has gone on a walk on a windy day and has allowed the wind to dictate where he goes. When the wind stops, he stops and puts his head between his knees. The only way the speaker can escape the all-consuming anguish is by removing it entirely from his focus and transferring that focus to close scrutiny of some object that is near to hand. For him, that object is the woodspurge, and his recognition of the woodspurge is the only thing he really retains from this terrible time in his life.
The Natural World
Even though the natural world is not literally a character in this poem, it does have a role that is at times more powerful than the speaker's own presence. The "wind," in the first stanza of the poem, is the catalyst for the speaker finding the woodspurge in the first place. Indeed, the wind seems to determine his direction; when it stops, so does he.
Additionally, although not addressed directly, the woodspurge is significant to the speaker in this moment of incredible grief. The speaker is able to focus on the woodspurge's three little cups with enough intensity to take him briefly outside of himself and the crushing weight of his grief. The woodspurge thus becomes, in a way, as vital and palpably real a character in both the moment and the memory of the moment for the poet.