The word snake never appears
The poem calls it a Fellow, a Him with a capital H, and later a transport of cord. Since the word snake is withheld, the reader has to supply it, and supplying it makes the reader complicit in the poem's alarm. That is a different effect from being told what to be afraid of.
Capitalising Him is a second manoeuvre. It gives the snake a social status, which is funny, and it also borrows the capitalisation convention of hymns and scripture — so the poem's dread has a faint liturgical echo without ever invoking God.
The last line is a sensation, not a feeling
Zero at the Bone is not an emotion word. It is a location and a temperature. By naming where the fear happens — the bone, the middle of the body — and giving it a number, Dickinson gets out of the trap that ruins most fear poems, which is announcing the fear instead of localising it.
Tighter breathing, two lines earlier, is the same technique in the body rather than the skeleton. Both lines are physiological. Neither says afraid, dread, terror, or fear. A reader who wants to know what the speaker feels has to deduce it from a chest and a bone.
Why the poem needs four stanzas to get there
The middle stanzas do a lot of quiet work: the snake's movement is described as a comb through grass, the speaker reports having been fooled by a whiplash, and crucially says that several people of her acquaintance feel a transport of cord. The fear is distributed. It is not one person's private phobia; it is a common response that everyone politely does not mention.
That distribution is what makes the last stanza land. Because the poem has already shown other people shrinking, Zero at the Bone is not a confession, it is a diagnosis. And notice the double negative in the last stanza — never met this Fellow / without — which means the poem's claim is that everyone feels it, stated in the most hedged grammar available.
A model to copy
If you are writing about something you are afraid of, do not name the thing. Name where in your body you feel it, and name one physical consequence of feeling it. Dickinson needs eight lines and no adjective for fear to be one of the most frightening poems in English.