Poor Old Horse - though not the shanty, which isn't about horses as such. As such it exists in various traditional versions - see Here.

A fine version was collected by Jim Eldon at the Appleby Horse Fair, here it is with extra verses from Grieg & Duncan

Poor Old Horse (The Old Grye Song).

Once he was a young horse, he was a young horse in his prime;
and his master used to ride him, and he thought he was very fine.

Chorus:
But he's still my own, bonny sweet, who rode so many the mile;
over hedges, ditches, brooks and bridges, gates and cleared many the stile.
Poor old horse, poor old horse, oh cherry old grey.

And his legs and his irons have all goe to decay;
likewise he poor old body, it's all withered away.

Once he wore the clothing of the lindsay oh so fine;
and his eyes they sparkle, and his mane it did shine.

Out from the warm stable to the fields he has to go;
let it rain, hail, or sun shines, or the winds blow high and low.

Oh, he's stealing all my hay, spoiling all my corn,
He's eating up the long grass that grows against the wall.

They'll beat him, whip him, cut him,
Til the huntsmen let him go.
Poor old horse, poor old horse, oh cherry old grey.