I have an (excellent!) copy of a copy of that New Yorker. besides the first two italcized paragraphs, the only difference I could find was---when she's listing the things they discussed on the "paw the white out of the moon" night, in the New Yorker, it says "military service," which she later changed to "draft."
The New Yorker gives no clue as to what the story will be about ("Cowboys and horses and long lonely nights in the wilderness") guess you can see that from jenny's page one. neat cartoon of Annie P, and I LOVE that illustration from another story, which I also have in my copy.