I'm a native speaker and it always amazes me how weird some of the grammars are for some everyday phrases.
I think this one is derived from a more traditional phrase, 吹风(since air conditioner is a relatively new thing), which is also weird because it is not to "blow the wind" but rather "get blown by wind".
A lot of weather related expressions have this grammar:
晒太阳 to be bathed by the Sun
淋雨 to be showered by the rain
To be honest I'm not sure why, maybe because the subject is "it"( mother Nature ) so it got hidden?
BTW, 南京大牌档 is the best, I went there a lot during my undergraduate study in Nanjing. Pretty authentic.