Forms of 'Poor Old Horse' (Roud 513) were found all over England and in the English-speaking areas of Wales, and was exported to the USA and Canada. In a band stretching from Yorkshire through Derbyshire and Cheshire into Northern Wales, the song was associated with a mummers' play featuring a 'mast' type horse (basically a pony's skull on a pole, set up so that the jaws could be opened and closed by an operator hidden under a blanket); the custom survived in the Sheffield area until the late 1970s or early '80s, and persists in parts of Cheshire. The song was also sung in many other parts of the country where there was no tradition of that sort, probably because it was widely printed on broadsides from the late 18th century well into the 19th.

'The Dead Horse' (Roud 3724) is less frequently recorded in tradition, known examples being mostly from the South of England and the Eastern USA. Parts of it seem to have been borrowed from the mummers' song (rather than the other way round). For some reason, the shanty seems to be better known in the Revival than the traditionally much more common land song; perhaps due to well-known recorded arrangements.

See other threads for more detail. 'Short grass' seems to be the most usual phrase.