The meter of The Railway Train alternates between tetrameter (four feet) and trimeter (3 feet). The pattern begins in the first line, which is tetrameter and is followed by a trimeter, followed by a tetrameter, with a trimeter to end the stanza. The pattern is followed throughout with incomplete feet at lines 5, 11 and 13, which end on a soft beat instead of a stressed beat of the iambic rhythm. The last two lines are a-metric and a-rhythmic except for the syllables, "stable door," which return to iambic and end the line, cadence of a trimeter (and can be read as a trimeter if the sentence stress is put in "its" instead of on "own." One metrical/rhythmic problem is that Dickinson disregards the "pause," or soft stress, value of a comma thus creating difficulties in lines 4, 6 and 14.
The overriding metaphor seems to compare the train to the concept of a horse. The "lap the miles," is referential to the horse on the track, and the first stanza's actions are all analogous to horses. In the final stanza, the idea of "neigh" is also something that makes the train similar to the horse. I think seeing it in this sense makes train transportation quaint and powerful.