The context is:
DAVID: I wish I had children.
FANNY: How could you? All the women you like are too drafty, if you know what I mean. None of them could have children. Which, as God in his wisdom, would have it.
I couldn't find in the Internet any definition of "drafty" except "cold and uncomfortable because of currents of cool air". Now, I understand there may be some sort of irony, but the comparing a draft and women who can't have children doesn't make any sense to me.