The New Lost City Ramblers recording is on the CD called The Early Years, 1958-1962. The album notes say the lyrics came from the Lomax book called Our Singing Country. Those lyrics are the same as what's in the Digital Tradition as When First To This Country - except that the DT & Lomax call it "When First To," and New Lost City Ramblers have it "When First Unto." Oh, and the Lomax book and the NLCR album have the horse described this way:

I rode to see my Nancy, the pride of my life,
Till I saw a fine gray horse, both plump-looking and white

The tune isn's quite what I remember. Maybe it's the Baez or Ian and Sylvia tune that's in my memory?
Hey - note that Lomax is scripturally incorrect. Grisman/Garcia correct the lyrics and speak of Joseph's coat.
-Joe Offer-