it's definitely for the japanse song, like piggleton pointed out.
"The black goat gets a letter from the white goat, but before reading the letter, they eat it. So they write a letter back to the white goat asking what was in the first letter. When the white goat gets the letter, they also eat it before reading. Then the white goat sends a letter back to the black one asking what their letter said.
This silly little song clears up all the portrait confusion, Chevre and Nan are pen pals. They write letters (and maybe eat letters) back and forth like the little goats in the song. It's another unique touch to Animal Crossing that many fans may have missed out on unless they were up to date on Japanese children's music."