This is all I found relevant to horses on the Watersons site:

Sung by Martin Carthy on Out of the Cut. The same recording is included on Martin Carthy's The Collection, and also on Martin Carthy's Rigs of the Time. Old Horse is also on Brass Monkey's Sound and Rumour, in a different performance, with almost exactly the same words. Martin Carthy also contributed this song to the Feed the Folk compilation of 1985. That recording is included in The Martin Carthy Chronicles.

OLD HORSE

Old horse old horse what brought you here
Carted stones this many's the year
Killed by stones and sore abuse
They salt you down for sailors' use
A warrior am I and at war I've been
Fighting for my country and king
Now I'm old and I'm in decay
It's poor old horse get on your way

My keeping once was the stable wall
Free from all cold winds and harm
Now in the fields I am forced to go
Turned out in the cold and rain and snow

My feeding once was the oats and hay
That grew in the fields and the meadows gay
Now I'll get no such at all
But pull at the short grass by the wall

The sailors they do me despise
Kick my body and damn my eyes
Cut my meat and pick my bones
Throw the rest to Davey Jones

Here is a hoof that was so well shod
Likewise a hide that sweat so hard
Whipped him lashed him drove him down
Rise up old horse and shine again

http://wwwmcc.murdoch.edu.au/~gillard/watersons/old.html