I am responding to Crowhugger's post (I hope I'm doing this right - I'm new here).
I agree with the additional layers you find.
Since the farmer is portrayed as the voice of self-justification and blaming-the-victim, it is criticism, and perhaps a suggestion that what is taken for granted - calves being led to slaugher - should not be taken for granted.
At the same time, the song deals with the opposing forces of fate, on the one hand, and striving to change it, striving to fly, on the other. Because there will always be some "farmer" out there, nor can you hope for help from the wind, which will only laugh...
I absolutely agree with the idea of the vicarious pleasure in the crow's flight, but it is also envy, and perhaps hope...

I find an interesting similarity between this motif and that of another famous musical-piece, of the same period:
"Somewhere over the rainbow
Bluebirds fly,
Birds fly over the rainbow,
Why, then, oh why can't I?"

"Over the Rainbow", of course, by Arlen and Harburg, published in 1939, the exact year when Dona Dona was written (though not yet performed). It may or not be a coincidence that "Over the Rainbow" was also written by two American Jews well immersed in East-European Jewish culture.