Down in Yon Forest in the modern form was collected by Ralph Vaughan Williams in Derbyshire in 1908. The earliest known version dates from the early 15th century (ca. 1504) is known as the Corpus Christi Carol because of the reference to Corpus Christi in the last verse. It does not have a specific Christmas reference, though.

There is a 16th century version which is apparently closer to the modern version but I haven't seen a copy of it.

John Jacob Niles collected a similar version to the Derbyshire one in N. Carolina. Both can be found at folkinfo.org

I copied the words of the Corpus Christi Carol from Wikipedia. (The Wikipedia article did not add very much else)

Lulley, lully, lulley, lully,
The faucon hath born my mak away.

He bare hym up, he bare hym down,
He bare hym into an orchard brown.

In that orchard ther was an hall,
That was hanged with purpill and pall.

And in that hall ther was a bede,
Hit was hangid with gold so rede.

And yn that bede ther lythe a knyght,
His wowndes bledyng day and nyght.

By that bedes side ther kneleth a may,
And she wepeth both nyght and day.

And by that bedes side ther stondith a ston,
"Corpus Christi" wretyn theron.