I've seen the kanji 風
appear in several different illnesses: [風邪]{«かぜ»} (a cold), [中風]{ちゅう・ふう} (paralysis), and [痛風]{つう・ふう} (gout). Conceivably there may be others, but I haven't seen them.
What does the wind have to do with any of these (aside from possibly catching a cold by going out into the cold wind—which I believe is a fallacy anyway)?
Update: Though I will not revoke the accepted answer, it seems it is only partially true. Recently I came across Miasma theory, and China is but one of several ancient societies where it was accepted.