From what I'm understanding in the first stanza, a women lost her lover to the war because he fell off his horse...Is that right?
Yes, Stephen Crane talks about lost love and sacrifices in his poem. The basic casualty of war. A lover, a father and son are lost in his story and those that are left behind he tries to console. The poem is noted for the ironic use of war is kind. We all know that War is really not kind. The poem’s speaker, simultaneously sympathetic with the victims of war and cynical about the purposes of war, implicitly criticizes the image of the romantic hero, showing in graphic scenes the realities of battlefield death and the emotional torment it causes for those left behind.
