They're catchy, short, and nearly impossible to forget. A good nursery rhyme tends to follow us through childhood and even into adulthood, mainly because of its singsong sound and repetition of key lines and imagery. Rossetti's "Who Has Seen the Wind?" fits the mold of the catchy nursery rhyme that you can't get out of your head after a few reads. If its not stuck yet, we dare you to give it a few more reads just to prove our point.
But why are nursery rhymes so annoyingly catchy? Just like a pop song you can't get out of your head no matter how hard you try, nursery rhymes use popular meters like iambic trimeter and iambic tetrameter to keep things sounding rhythmic and predictable. Perfect end rhymes like you/through and I/by also help to keep the poem sounding songlike and catchy. You can easily anticipate the sound of the next syllable once you hear the up/down or down/up pattern a few times. Being able to predict what comes next can be a useful learning tool for kids who usually pick up on patterns pretty easily.
So the magic of Rossetti's poem is really in the meter and repetition of the speaker's pressing question. The first two lines of each stanza are written in that headless iambic trimeter while the following lines are in iambic tetrameter and iambic trimeter respectively. Once we've heard the first stanza, we can pretty much predict that the following stanza will follow the same sound pattern, like most nursery rhymes. All the speaker had to do was remove the heads of that initial iambic trimeter pattern to make the sound move from up/down to down/up. So in a way, the poem's meter acts like a call and response: the first two lines ask the question while the following lines answer. Neat, huh?