Lyrics published in Sing Out! in the 1970s went like this:

RATTLESNAKE

Rattlesnake oh rattlesnake,
What makes your teeth so white?
I been in the bottom all my life
And I ain't done nothin' but bite, bite,
Ain't done nothin' but bite.

Rooster oh rooster,
What makes your claws so hard?
Been scratchin' in gravel all my days,
It's a wonder I ain't tired, (tard), tired
A wonder I ain't tired.

Jaybird oh jaybird,
What makes you fly so high?
Been robbin' your cornpatch all my life,
It's a wonder I don't die, die,
A wonder I don't die.

Groundhog oh groundhog,
What makes your back so brown?
It's a wonder I don't smotherfy,
Livin' down in the ground, ground,
Livin' down in the ground.

I'm pretty sure there was a muskrat verse too, but none of those mentioned here ring much of a bell.