The wind might be invisible, but that's not to say we can't feel it and see how it affects the rest of nature. That's kind of what makes nature so mysterious, since we usually only get a glimpse into the ways of nature.
But when the leaves hang trembling, The wind is passing through. (3-4)
It's those leaves that tell us that the wind does in fact exist in the poem. Their "trembling" is our only evidence of the wind's mysterious ways. So man might not be able to see the wind, but at least nature is throwing us a bone here through the leaves.
But when the trees bow down their heads, The wind is passing by. (7-8)
Nature also seems to have a kind of understanding that man just doesn't get. The trees "bow down their heads" like they know what's up. They respect the wind and don't fuss and fight when it passes by.