For anyone who's interested, I have just borrowed Cecil Sharp's 'English Folk Songs' (same contents as his One Hundred English Folk Songs'), as luck would have it, and in it is a Warwickshire version of Poor Old Horse. The words are quite similar to the above and scan the same (except there is only one "Poor old horse!" refrain at the end of the verse), and there is a tune included. The tune is a very close relative of one of the well-known 'Derby Ram' tunes.