Elizabeth Poston wrote in her Second Penguin Book of Christmas Carols (p. 28):

Suitable for all times and seasons, this song is not specifically a Christmas song. It is included here because of its association with Christmas in the carol services and broadcasts of the choir of King's College, Cambridge, who have also recorded it (EMI ALP/ASD 2290). The beautiful visionary words in the imagery of the Tree of Life are printed without tune in Johua Smith's Divine Hymns or Spiritual Songs, Portsmouth, New Hampshire, 1784.

Tune (midi & score) of "Jesus Christ, The Apple Tree" is here, where it is said to be "traditional."