What exact style of poem is "A Narrow Fellow in the Grass," free style or blank verse, rhyme maybe?
Dickinson's meter is famously irregular, but one way to think of it is as a form of ballad meter, which uses alternating lines of iambic tetrameter and iambic trimeter. There are examples in the first two stanzas of this meter:
a NAR row FEL low IN the GRASS
o CCAS ion NAL ly RIDES
or, second stanza
the GRASS di VIDES as WITH a COMB
a SPOT ted SHAFT is SEEN
Dickinson doesn't really follow all the "rules" for ballad meter. For one thing, ballad meter generally follows an ABCB rhyme scheme, but in the poem only the final two stanzas follow this pattern. And Dickinson uses many lines that depart from the iambic tetrameter/trimeter scheme.
Less important than a technical analysis of meter is an appreciation of how Dickinson's rhythm affects the meaning of the poem. If you read the poem aloud, it's clear that there is a kind of jerky quality to the rhythm, as Dickinson adheres to and departs from the ballad meter form. This quality reinforces her dream-like meditation on the snake (is it a snake or a whip? Is nature "cordial" or frightening?).