I think that you could argue this a few of different ways. You could say that the phrase "narrow fellow" is a metaphor or you could say that it is personification. But I would argue that this is actually a euphemism.
You could say this is metaphor because the snake is being compared to a skinny person. Both share the characteristic of being skinny.
You could say it is personification because the snake is being referred to in human terms -- it can ride, for example.
But I think it is euphemism because Dickinson is trying to dance around saying "snake" because she does not like snakes. I think that this feels more like euphemism because she is trying not to say a word that is repulsive to her.
The term is anthropomorphism. Personification is ascribing human characteristics (physical), while anthropomorphism ascribes (psychological) characteristics as well.
“Fellow” (and the pronouns “Him” and “His,” rather than “it” and “its”) and “rides” in the first stanza help to assimilate the snake to the human world, as does “comb” in the second stanza. In these two stanzas there is some emphasis on the unexpectedness of the snake. He is “sudden” but not menacing. And in the beginning of the third stanza he seems almost an eccentric neighbor: “He likes a Boggy Acre.” In the fourth stanza the reference to a whiplash introduces a more threatening note; “Nature’s People” in the next stanza seems to bring us back to the comfortable world of the first stanza, but with the last line of the poem (“Zero at the Bone”) there is communicated a terror that indicates a response to the snake as supremely hostile.
(The snake is, after all, a traditional image of our satanic enemy.) The contrast between “a transport / Of cordiality” (which carries a sense of warmth, that is, warm-heartedness, via cor, heart) and the coldness of “Zero at the bone" could hardly be greater.