Does wind and wing rhyme

Depends on whether wind is used as a verb or a noun. As a verb "to wind", they would rhyme.

As a noun, "wind" is the one Word ending in "-ind" that doesn't rhyme with the rest of the group (blind, mind, kind, find, hind, grind etc.)

However, in Shakespearean times they do, examples are such as in The Tempest,

"Arise ye subterranean winds,

More to distract their guilty minds!" and so forth, suggesting that back in the days English language is a bit more consistent.