So, on the article talk page, I suggested that the original article should be restored, and if the editor in question felt that the article should still be deleted, he should submit it to AfD himself. He didn't, but suggested that I submit it to AfD.
So although I didn't agree at all with the "article is unencyclopedic" position, I submitted it to Articles for Deletion anyway. I did this hoping that there would be enough support for the article to fend off any further suggestions for deletion. This strategy seems to have worked very well, and during the process the article was improved with real media citations.
While I agree that in general, Wikipedia should not be a general repository for jokes and memes and whatnot, this particular joke has been around long enough, well outside the context of "the internet", that it has become notable. It's nice to have this solidified in the history of Wikipedia.
THE COWS ARE OK.