We don't know for certain.
Green light in Lord of the Rings is primarily associated with Gollum; particularly the colour his eyes take on when his evil side is in control:
Gollum was talking to himself. Smeagol was holding a debate with some other thought that used the same voice but made it squeak and hiss. A pale light and a green light alternated in his eyes as he spoke.
Suddenly he turned back. A green light was flickering in his bulging eyes. 'Masster, masster!' he hissed. 'Wicked! Tricksy! False!' He spat and stretched out his long arms with white snapping fingers.
Howeve, Tolkien uses the very same green light to describe Treebeard, so we definitely shouldn't read anything significant into the choice of colour:
But at the moment the hobbits noted little but the eyes. These deep eyes were now surveying them, slow and solemn, but very penetrating. They were brown, shot with a green light.
One possible connection is in the following description of Minas Morgul, where it's glowing colour is likened to the green light in Gollum's eyes:
Then his eyes shone with a green-white light, reflecting the noisome Morgul-sheen perhaps...
As we know, the Barrow-wights were sent by the Witch-king, thus establishing the connection between Minas Morgul and the Barrow-downs:
It was at this time that an end came of the Dunedain of Cardolan, and evil spirits out of Angmar and Rhudaur entered into the deserted mounds and dwelt there.
And so the green light may be indicative of this connection, but there is really no other evidence to suggest anything.