Someone posted somewhere that the words were written by Cicely Fox Smith. I doubted this, but then the same assertion came up in uk.music.folk, so I e-mailed Danny McLeod, who may be the leading authority on C.F. Smith.

He told me the name of the poem was 'Homeward' and it had been written by C.F.S.
It appears in her book of poetry 'Fighting Men' published in 1916, and also was included in her book 'Songs and Chanties 1914-1916' published in 1919 by Elkin Mathews (London) which was a compilation of her works, 'Songs in Sail' (1914), 'Sailor Town' (1914), The Naval Crown'(1915), and 'Fighting Men' (1916).

Danny found and purchased the original manuscript (in her own handwriting) of many of her earlier poems written prior to 1920. This poem is among them.
Danny said he'd talked to Sarah Morgan and that she'd discovered it in the magazine 'This England' (1984) and it had been entitled 'Going Home Together'. The writer had been a soldier, who credited the poem to "anonymous." The first line had been changed, possibly by that soldieer, to be about India, and the horses names were changed, possibly to ones the soldier was familiar with. The second verse is typically used as a chorus in the more well known version of the song.

Per Danny McLeod, here is the poem as it was written. (And many, MANY thanks to Danny for sharing this wealth of information!)

HOMEWARD
Words: C. Fox Smith, Tune: Sarah Morgan

Behind a trench in Flanders, the sun was dropping low,
With tramp and creak and jingle I heard the gun teams go;
And some thing seemed to 'mind me, a-dreaming as I lay,
Of my old Hampshire village at the quiet end of day.

Home, lad, home, all among the corn and clover!
Home, lad, home when the time for work is over!
Oh, there's rest for horse and man when the longest day is done,
And they go home together at setting of the sun!

Brown thatch and gardens blooming with lily and with rose,
And the cool shining river so pleasant where he flows,
Wide fields of oats and barley, and elderflower like foam,
And the sky gold with sunset, and the horses going home!

Old Captain, Prince and Blossom, I see them all so plain,
With tasselled ear-caps nodding along the leafy lane,
There's a bird somewhere calling, and the swallows flying low,
And the lads sitting sideways, and singing as they go.

Well, gone is many a lad now, and many a horse gone too,
Of all the lads and horses in those old fields I new;
There's Dick that died at Cuinchy, and Prince beside the guns,
On the red road of glory, a mile or two from Mons!

Dead lads and shadowy horses --- I see them just the same,
I see them and I know them, and name them each by name,
Going down to shining waters when all the West's aglow,
And the lads sitting sideways and singing as they go.

Home, lad, home . . . with the sunlight on their faces !
Home, lad, home . . . to the quiet happy places!
There's rest for horse and man when the hardest fight is done,
And they go home together at setting of the sun!

^^