First, it is important to keep in mind that Shakespeare relies heavily on the principle that the form of the poem reflects its function and content.
Venus and Adonis is written in the minor epic style popular at the time, which involved giving side characters from legends and myths their own small "epic." Thus, according to convention, Shakespeare wrote the story in narrative form, a series of stanzas that make the story easier to follow through segmentation and simple rhyme schemes (this poem is mostly ABABCC). In the minor epic style, the writer gives agency to these minor characters through giving them their own story, or fleshing out what little we know of them from the major myth. Thus, it can be expected that the major players are those characters and whomever is influencing them (often gods). However, here Shakespeare is giving agency to nature through the continuous comparisons, making the poem also function as a pastoral.
In pastorals, nature is typically beautiful and calm (and Venus is the goddess of beauty), but Shakespeare reflects that it is also primal through Venus's lustful and aggressive love for Adonis. In the poem, this aggression reflects the epic nature but is also contained by the strict rhyme scheme and the convention of the pastoral poem.
Therefore, the nature presented through convention as beautiful, and through Shakespeare's graphic tale as primal, serves to tie the story back to both pastoral and minor epic connotations. Nature is so present so that Shakespeare can show how it is subverted and manipulated through the agency of the actors in the poem, as well as how the actors themselves are restricted and confined to natural tendencies. The poem asks us through the comparisons to nature if nature or the characters Venus and Adonis have more power.