Mr Flibble,

This was originally a pagan song.

A quick search produces numerous variants on the verse you mention. Three examples:

Oh, the rising of the sun
And the running of the deer
The shining of the winter stars
As the longer days draw near

Oh, the rising of the Sun
And the running of the deer
The turning of the winter season
Sweet singing all may hear

Oh the rising of the sun
And the running of the deer
The harvest bride shall be brought to bed
And we shall have good cheer

Which is the oldest? No idea, I'm afraid...