What do the metaphors, "peppermint wind, asphalt flowers, and chalk-white arrows" mean in the poem "Where the Sidewalk Ends"?
In the poem Where the Sidewalk Ends, author Shel Silverstein is essentially suggesting that there is a magical place that children know of "where the sidewalk ends." That place represents childhood, its innocence, and its fundamentally different way of looking at the world (as opposed to the way that adults view it).
The metaphors that you cited help the reader to visualize the differences between the adult world and this child-centered world. The world where the sidewalk ends is filled with pleasant imagery, such as grass that grows "soft and white" and a bright crimson sun. The "peppermint wind" is likewise pleasant. Like eating a mint, a peppermint wind would be cool and refreshing. If you are old enough to remember York Peppermint Patty commercials, that is the idea. A cool, refreshing breeze in a pleasant place.
By contrast, the land inhabited by the adults is filled with dark imagery -- "black smoke" and "dark roads." The reference to "asphalt flowers" tells the reader that even those things that would typically brighten up such a place -- flowers, perhaps, in front of an otherwise drab building -- are likewise grey or absent altogether. In the adult world, everything is grey and unchanging.
Silverstein urges the adult reader to enter the land of children "where the sidewalk ends." He mentions that chalk-white arrows will lead the way. One can imagine children bent over on the blacktop, drawing arrows with sidewalk chalk to lead the way. Chalk is typically associated with children, and Silverstein very deliberately uses chalk to conjure images of children guides who will ultimately lead the way.
In summary, then, Where the Sidewalk Ends contrasts the world of the adult with the world of children, where the sidewalk ends. The metaphors you mentioned (explained above) help to strengthen the contrast between the two.
For full text of the poem, please refer to the poems.org website below.