Worldcat.org lists two copies of the sheet music.

WISE OLD HORSEY
Words and music by George M. Fraser, [ca. 1937-1938]

One copy is marked 'Theme song of the Oxford Group film "Youth Marches On.'

The other copy is marked (according to the catalog) 'Theme Song of the Oxford Group Sound Film "New Frontismen".' [sic; should be "Frontiersmen"]

IMDb.com has this comment about "Youth Marches On" (1938) – a 20-minute documentary:

"A documentary about the Oxford Group, a propagandist spiritual-movement, for young men and women, with its origins in England. Their message was a cheery exposition of brotherhood and unselfishness of one-and-all lending a helping hand to their fellow man, which would make all lives brighter and easier. A Canadian cowboy joins up and goes to London with a group of young men, and his horse, to spread the Oxford Group's gospel throughout the Empire."

George Fraser is listed as producer and co-writer of "Youth Marches On."

I couldn't find any IMDb listing for the other film.