What are the figures of speech used in the poem? What are the symbols used and to what do they refer?

In this poem about horses, Larkin uses synecdoche, a term which means that the part stands in for the whole. First, he lets us know he is talking about horses by referring to them not as horses, but by their parts: "tail and main." He also puns on the word "main" as a horse's mane is spelled differently. Through the pun or double meaning, he perhaps likens the horses to ships in the wind. Larkin also uses synecdoche when, instead of referring to people coming to the races, he refers to them as "parasols." This economy of language communicates that people are watching the races but also offers us an image of women holding parasols, setting this scene in the past. Later, words like "fieldglass" and "stop-watch" stand for humans.
Larkin uses simile, a comparison using like or as, in the line

Do memories plague their [the horse's] ears like flies?

The poem also employs rhyme to impart a sense of rhythm, such as "sky" and "cry" and "heat" and "street" in the third stanza.
The poem's main symbol is the horses. They are retired and put out to pasture. They symbolize or stand for humans. Like the horses, we too move past our glory days and can enjoy our retirement. The horses are a primarily positive symbol of aging, for they

stand at ease, Or gallop for what must be joy ...