Shelley's "Ode to the West Wind " uses symbolism throughout to convey its primary theme of the sublime power of nature. You are correct in stating that the West Wind is used symbolically, but it is not necessarily "a symbol" as such—Shelley is, indeed, literally addressing the wind, but...
Shelley's "Ode to the West Wind" uses symbolism throughout to convey its primary theme of the sublime power of nature. You are correct in stating that the West Wind is used symbolically, but it is not necessarily "a symbol" as such—Shelley is, indeed, literally addressing the wind, but the personified West Wind also represents a host of other elements in the world of weather and nature, which govern the world humans inhabit. Shelley's personified West Wind falls in line with a very common Romantic trope, pathetic fallacy, wherein weather and the natural world are given human attributes, with their behavior reflecting changes in the wider environment.
In the first section of the poem, the Wind symbolizes a dual force of destruction and creation, "Destroyer and preserver." Allusions in this section suggest mythical elements; the Wind "chariotest" the dying plants of autumn to their winter rest, and it is addressed as "Wild Spirit," with both of these elements redolent of classical mythology. Similarly, the West Wind's "azure sister of the Spring" is mentioned, indicating that the West Wind is only one of nature's children.
Quasi-Classical allusions recur throughout the poem to emphasize the godlike power of the West Wind: it "did waken...the blue Mediterranean" and its "voice" causes the oceans to "tremble" with fear. In this section, the Wind symbolizes a force "uncontrollable" enough to make the rest of the natural world fear its whims.
In the final stanza, however, the Wind symbolizes something else, as the speaker calls upon it to "be thou me, impetuous one!" Here, the Spirit symbolizes the artist's muse or inspiration, which will drive away "dead thoughts" like dead leaves in order to help the artist "quicken a new birth" of thought. At this point, then, the poem cycles back to its point of origin, with the West Wind symbolizing the destruction of what has had its day, and the creative force that helps birth the new.