[Alcuin]

The green light in the barrow serves two purposes.

• The barrow, of course, is naturally dark, like the inside of a cave – or a cow. There are no torches, the tomb is sealed (how the barrow-wight exited and entered the barrow, especially with the hobbits, is not explained), and covered above with earth. While many real barrows were built with wood, I think this barrow is constructed of megaliths (especially large stones). If there is no light, all the action will take place in the dark, and Frodo will be at too severe a disadvantage. So the green light plays an important part in the telling of the tale.
• The green light is almost unquestionably a “corpse light,” like unto a will-o-wisp, which might be blue or green in color.

Green lights were in the late nineteenth century associated with ghostly visions and with the appearance of the dead. Consider this from Chapter 2 of Oscar Wilde’s The Canterville Ghost, published in 1887:

For a moment the Canterville ghost stood quite motionless in natural indignation; then, dashing the bottle violently upon the polished floor, he fled down the corridor, uttering hollow groans, and emitting a ghastly green light.

In H.G. Wells tale The Plattner Story, published in 1896, the protagonist experiences an explosion in which he enters a world in which others (presumably the dead) can watch our world but have no influence upon it. That world is illumined with a green light.

From “Unseen — Unfeared” by Francis Stevens (pseudonym for Gertrude Barrows Bennett, 1884-1939?), originally published in People's Favorite Magazine (10 February 1919),

Green light is peculiar. It may be far fainter than red, and at the same time far more illuminating.

The green light, in my opinion, harkens to a tradition that decaying matter can produce a greenish glow.

It has been recently noted by Raynor elsewhere in the Forum that Tolkien had probably visited Wayland’s Smithy, a barrow predating the Anglo-Saxons that they attributed to their (Nordic) god Weyland the Smith. Wikipedia reports a Shropshire legend in its will-o-wisp article about a certain “Will the Smith” who is doomed to wander the earth with a coal he uses to lure travelers to their demise. You can read an excellent, short synopsis of the barrow and its history, and see a diagram of its layout here. Notice in this article that “an area of the burial chamber was known as snivelling corner,” reminiscent to me of Tolkien’s description of the wight after Frodo struck it with the sword he found:

With what strength [Frodo] had he hewed at the crawling arm near the wrist, and the hand broke off; but at the same moment the sword splintered up to the hilt. There was a shriek and the light vanished. In the dark there was a snarling noise.

Note also that the sword “splintered up to the hilt,” much like the barrow-blade which withered after Merry smote the Witch-king, the Morgul-knife which melted after it had been used to strike Frodo, and especially Éowyn’s sword when she decapitated the injured Witch-king (Return of the King, “The Battle of the Pelennor Fields”): “The sword broke sparkling into many shards.”

Because it may have influenced Tolkien’s imagination of the barrow, here are images of Wayland’s Smithy in poor lighting and fog:

Frodo was not seized with the other hobbits, but separately from them. They have already been captured and arrayed in the apparel of the dead buried in the tomb. The wight before it places its hands upon Frodo says to him, “‘I am waiting for you!’” Indeed it is, for we are told in Unfinished Tales, “The Hunt for the Ring”, that the Witch-king was responsible for sending the wights into the barrows after the Great Plague of III 1636, and that in September III 3018, when the Nine finally found “Shire” and prepared to flush out the Ring-bearer,

…he himself visited the Barrow-downs. In notes on the movements of the Black Riders at that time it is said that the Black Captain stayed there for some days, and the Barrow-wights were roused, and all things of evil spirit, hostile to Elves and Men, were on the watch with malice…

Reader’s Companion notes that the disembodied hand of the wight resembles Tolkien’s painting of Maddo in Tolkien Artist & Illustrator, plate number 78, which they describe (p. 35) as

a bogey … that was imagined and feared by Tolkien’s second son, Michael, when he was a child.

Hammond and Scull in almost the very last sentence of their chapter on Tolkien’s art for “The Lord of the Rings” note that a “sinister hand” is depicted by Tolkien in another early drawing, Wickedness, in Maddo, on Thror’s map in The Hobbit, and in plate 181, a preliminary sketch for an abandoned dust-jacket for The Return of the King depicting the scene in the chapter “The Field of Cormallen” when Gollum falls into the Cracks of Doom with his Precious:

… as the Captains gazed south to the Land of Mordor, it seemed to them that, black against the pall of cloud, there rose a huge shape of shadow, impenetrable, lightning-crowned, filling all the sky. Enormous it reared above the world, and stretched out towards them a vast threatening hand, terrible but impotent: for even as it leaned over them, a great wind took it, and it was all blown away, and passed; and then a hush fell.

The picture, I believe, is a possible guide to how Tolkien envisioned Sauron, and certainly how he envisioned this scene: I am not aware that he ever again attempted to depict that Umaia in art.

Frodo and his burden were, I believe, what the wight wanted: whether the wight was conscious of the Ring or not, it obeyed its master, the Witch-king, and it recognized that Frodo was different from the other three hobbits, whom it sought to offer as human sacrifice to the Darkness (presumably Morgoth or Sauron). Had Frodo put on the Ring in the barrow, I do not believe he could have escaped: he would have seen the wight in the shadow-world as he later saw the five Nazgûl on Weathertop: the wight could have seized him then and there, and held him until the Witch-king arrived to retrieve his goodies. In fact, when Frodo awoke in safety in Rivendell, Gandalf told him (Fellowship of the Ring, “Many Meetings”):

...you have some strength in you, my dear hobbit! As you showed in the Barrow. That was touch and go: perhaps the most dangerous moment of all. I wish you could have held out at Weathertop.