This is sort of a trick question as Moore's metaphor comparing nature to love has a more complex and subtle realization than a simple "how nature is used as a metaphor for love." This extended metaphor of nature compared to love is the primary metaphor upon which the whole poem is built. Additionally, it is the primary metaphor for the metaphorical variations in each stanza, each of which varies the nature/love metaphor.
As the poem's overall metaphor, the comparison of nature to love is realized starting at the first line when Moore compares his aged beloved to "the last rose of summer / Left blooming alone." We know this is an aged beloved because stanza two turns to the topic of death through the metaphor comparing sleep to death: "Go sleep thou with them. / ... / [Who] Lie scentless and dead." The end of the overall metaphor is the last lines of the third stanza when Moore, via his poetic voice, laments inhabiting "this bleak world alone" when all loved ones are dead and gone.
The nature/love metaphor is developed in the variations on the theme in stanzas two and three. As discussed above, stanza two turns nature/love to a comparison between nature and death, with a complex metaphor added that compares sleep to death. The continuation of nature in the metaphor is established first in the line "To pine on the stem," while the introduction of death comes first in the line "Since the lovely [roses] are sleeping." The meaning of "sleep" is confirmed (for those in doubt) in the line "Lie scentless and dead."
Stanza three introduces another variation in a comparison of nature to [bereaved] loneliness. The words that establish the loneliness portion of the metaphor are decay, drop away, lie wither'd, flown, bleak, and alone. The words that confirm the nature portion of the metaphor, and which may overlap with words signifying the other portion, are shining circle, gems, wither'd (i.e., leaves), flown (i.e., birds), and world (i.e., nature). Moore's illuminating intricate and complicated extended metaphor has complementary extended metaphors, which are variations on the original, embedded within the primary metaphor comparing nature to love.