The tone at the beginning of the poem seems relaxed and matter-of-fact. This is in large part because the poem is narrated in the past tense, meaning that there is now a distance between the speaker and the events she describes, which allows her to describe those events with a degree of detached objectivity. Words like "kindly" and "Civility" describing "Death" also lend to the tone of the poem a suggestion of gratitude. This is slightly undermined, however, by the fact that "Death" is so immediately prominent. The tone of the poem in the beginning (relaxed, matter-of-fact, grateful) seems conspicuous because of the prominence of "Death," and the reader perhaps senses that this initial tone might be misleading.
By the fourth stanza, vocabulary like "quivering," "Chill," and "Gossamer" connotes a more sinister tone. At this point in the poem, the reader may be aware that "Death" is taking the speaker towards her own death, and this knowledge will affect the tone of the reader's voice and compound the change to a darker, more sinister tone.
At the end of the poem we realize that the narrator is in fact dead, narrating the poem from the afterlife. This may suggest that the tone becomes darker still. However, the final lines of the poem, "the Horses' Heads / Were towards Eternity," actually implies a more peaceful, hopeful tone. The implication of the final lines is that the speaker's earthly death was only the beginning of an eternal life in the spiritual realm. The speaker lives on, and this ensures that the tone of the poem at the end is hopeful, if not exactly happy.