This song has some uncanny resemblances to Secret Prayer (which starts off "There is an hour of peace and rest, unmarred by earthly care . . ."; plus, it ends phrases at times with the words heav'n and giv'n; the way the music to the tune of Woodland sounds also seems related). Anyway, just a thought - perhaps the writers of Secret Prayer knew of this hymn.
This hymn (The Hour of Peaceful Rest), however, is not about prayer - but, it is about the peaceful rest that can be found in heaven.
If anyone can find out where SATB parts for this song are that correspond to the tune Woodland as seen in The Hour of Peaceful Rest (AKA There Is an Hour) in the 1844 LDS hymnal I would be very grateful. The nwc file at the Cyberhymnal has different parts altogether. I suspect the version in the LDS hymnal was in fact originally written with all four parts, as the bass part on another from this book (Yes, My Native Land, I Love Thee with the tune Greenville) corresponds with the bass part on four part versions elsewhere (including the nwc for Greenville at the Cyberhymnal, in the article for Lord, Dismiss Us with Thy Blessing).