I tried to track down the song called WEEP, O WILLOW mentioned by Guest,Nancy above.

WorldCat.org reports that several college and university libraries have the sheet music, described thus:

WEEP, O WILLOW : for mixed voices
arranged by Sven Lekberg
Evanston, Ill. : Summy-Birchard, ©1957.
SSAATTBB and S solo.
Piano for rehearsal only.

The only recordings available seem to be by various high-school and college choirs.

Several performances are viewable on YouTube.

After listening to one of them, I conclude it is NOT the song we are looking for. It would be hard to transcribe, but I'm pretty sure there is no mention of a horse.