Ballads of The North Countrie compiled by Graham R. Tomson and published by The Walter Scott Publishing Co. Ltd. has a version titled "A Lyke-Wake Dirge". Words similar to those on the Pentangle recording but attributed to having been culled from Border Minstrelsy, Volii, p. 357."Whinny-muir" is spelled as before but with a hyphen (as is Lyke-Wake) The book I refer to has no publishing date(?) but is probably from the early 20th century.
I was told by an elderly aunt that whinny was a varient of whining due to the prickly heath scratching one's skin.
therefore a muir (or moor) with plants that made one whine when one came into contact with them. Like stinging nettle?