Joe, you were right the first time. The song is a variation of The Cherry Tree Carol. I found the words on the Net, although this is different from the one I knew.

I am not satisfied that this is the version I used to sing in the choir, but it is certainly close. It seems to me that verses one and two go together, and should be something akin to verse one in front of verses three and four, because verse one is sung differently than the other three. I think each of them is supposed to start with four lines akin to verse one beginning "As Joseph was a-walking", although he sees or hears something different each time.

The Cherry Tree Carol
Traditional

As Joseph was a-walking
He heard an angel sing
"This Night shall be the birth time
Of Christ, the heavenly King

He neither shall be born
In house nor in hall
Nor in the place of paradise
But in an ox's stall

He neither shall be clothed
In purple nor in pall
But in the fair white linen
That usen babies all

He neither shall be rocked
In silver nor in gold
But in a wooden manger
That resteth on the mould