There seems to be critical agreement that "Ariel" is ostensibly about Sylvia Plath's horse, although at the word "Shadow," she changes her focus to a metaphysical, symbolic one. The only way to begin to (hopefully) grasp this highly symbolic and suggestive poem is to look up every key word and try to find a metaphorically suggestive meaning. Also integral to understanding is a knowledge of the (true) legend of Lady Godiva and the fairytale story "The Little Mermaid," as Path uses allusions to both of these to make her point.
Which is a good place to start: Plath's point seems to be that stripping away materialism (hands, stringencies) leads to immersion in something larger than self (sea) for a larger purpose than material gain (which is "shadows") and leads to the intellectual and aesthetic judgments (eye) of a new beginning (morning).
Space doesn't permit a thorough analysis, but we can make a start together. Plath uses highly metaphorical language. In Stanza 1, note that "stasis" suggests motionlessness in the night (blue) where there continuously appear (pour) high rocks and hills (tor), symbolizing obstacles and journies encountered. Recall that this is in night, the opposite of "morning."
Stanza 2 seems to be a straightforward reference to the experience of riding a horse which Plath becomes at one with, while her worries (furrow) are torn away and she feels kinship (sister) with the horse. The next four lines detail the experience of material life through the symbolic representation of eating a blackberry. At the word "Shadows." the metaphysical shift occurs.
The shift takes the reader from real life experience to symbolic and spiritual experience. The irony is that Plath represents the material experience as shadows, unreal, compared to the spiritual (Something else) that compels her (hauls me). The Lady Godiva allusion sets up the image of a woman who protests materialism (taxes against Coventry), sacrificing her self-dignity and honor to ride unclothed, bare, exposed through the populace. This is a metaphor symbolized by "dead hands," the symbol of collecting taxes, and "dead stringencies," the symbol of rigorous requirements pertaining to money: materialism.
Now comes the little mermaid allusion in which Plath throws herself into the sea in a symbolic act of self-purging and self-sacrifice that is the result of protesting and rejecting materialism in the Godiva allusion. In this act, Plath becomes part of the vast and mighty ocean (a glitter of seas), while the child's cry of protest--symbolic of innocent ignorance--vanishes from hearing (melts in the wall).
With "And I" Plath describes her transcendence following this self-sacrifice. She is metaphorically an arrow, meaning she moves with the speed of an arrow; she is also metaphorically the dew of sea spray that speeds from the ocean after her plunge of self-sacrifice (suicidal). She has come to be at one with the drive into enlightened intellectual and aesthetic judgments (eye) that proceed from (cauldron: brew) a new beginning (morning). With this, she moves from night (ignorance) to day (enlightenment).
The latter half is unified with the first half through the ideas of speed (horse, Stanza 3; arrow; dew that flies) and the concept of being at one. In the first half, she is at one with the horse, in the latter, with the drive to enlightenment.