Green’s Dictionary of Slang

dismissive phr., usu. as ‘I would sooner...’ .

1647		Beaumont & Fletcher Humorous Lieut. in Works (1750) III 24: If ye catch me then, / Fighting again, I'll eat Hay with a Horse.
1659		J. Day Blind Beggar of Bednall-Green 108: Give me but an ashen Gibbet in my hand, and I do not dry-bang them both I’ll be bound to eat hay with a horse.
1815		‘C. Lark’ Paddy Hew xii: I'd eat hay with a horse before I’d write a preface.
1840		C.F. Hoffman Greyslaer I 38: May I eat hay with a horse, if I suffer such a thing among my riders.
1877		Coventry Times 10 Oct. 6/4: He refused me in anger, saying, I would sooner eat hay with a horse.
1886		Sunderland Dly Echo 21 Apr. 3/5: Defendant roustly declared he was a liar, and offered if the officer could prove what he said, to eat hay with horse.