What were the two standing stones that Frodo sees?

Question

In the Lord of the Rings (Fellowship of the Ring), in the chapter The Fog on the Barrow-downs, the hobbits fall asleep on a saucer-like topped hill and awaken as the sun is setting. Alarmed, they attempt to march onwards, towards the northern boundary of the Barrow Downs.

This is written, as they continue their journey:

Their going was very slow. To prevent their getting separated and wandering in different directions they went in file, with Frodo leading. Sam was behind him, and after him came Pippin, and then Merry. The valley seemed to stretch on endlessly. Suddenly Frodo saw a hopeful sign. On either side ahead a darkness began to loom through the mist; and he guessed that they were at last approaching the gap in the hills, the north-gate of the Barrow-downs. If they could pass that, they would be free. 'Come on! Follow me!' he called back over his shoulder, and he hurried forward. But his hope soon changed to bewilderment and alarm. The dark patches grew darker, but they shrank; and suddenly he saw, towering ominous before him and leaning slightly towards one another like the pillars of a headless door, two huge standing stones. He could not remember having seen any sign of these in the valley, when he looked out from the hill in the morning. He had passed between them almost before he was aware: and even as he did so darkness seemed to fall round him. His pony reared and snorted, and he fell off. When he looked back he found that he was alone: the others had not followed him. 'Sam!' he called. 'Pippin! Merry! Come along! Why don't you keep up?' There was no answer. Fear took him, and he ran back past the stones shouting wildly: 'Sam! Sam! Merry! Pippin!' The pony bolted into the mist and vanished. From some way off, or so it seemed, he thought he heard a cry: 'Hoy! Frodo! Hoy!' It was away eastward, on his left as he stood under the great stones, staring and straining into the gloom. He plunged off in the direction of the call, and found himself going steeply uphill.

After they are rescued by Tom Bombadil, Frodo looks for the standing stones, but he cannot see them:

At last they set off. They led their ponies down the hill; and then mounting they trotted quickly along the valley. They looked back and saw the top of the old mound on the hill, and from it the sunlight on the gold went up like a yellow flame. Then they turned a shoulder of the Downs and it was hidden from view. Though Frodo looked about him on every side he saw no sign of the great stones standing like a gate, and before long they came to the northern gap and rode swiftly through, and the land fell away before them.

Were the two standing stones indeed the entrance to a barrow? Had the hobbits perhaps become disoriented in the fog and were moving towards the east and towards a barrow? Or, may this have been some sort of supernatural element (a mirage of sorts), having something to do with the Witch King's recent visit to the barrow-downs and summoning/re-awakening of the evil spirits?
The absence of the standing stones the next morning makes me wonder if indeed the stones were some sort of apparitional object, if not an actual barrow.

Answer 1

This is one of only two places this is mentioned in the Legendarium and earlier versions of the Lord of the Rings.

Neither of the mentions gives us any insight into what they may be. However if they're anything like the rest of the standing stones, they may simply be signposts for the location of a Barrow, as suggested by the earlier spotted standing stones. Although like various things in the Barrow, they may be magical and appear and disappear depending on the need to "capture" a wayward traveller.

But even as he spoke he turned his glance eastwards, and he saw that on that side the hills were higher and looked down upon them; and all those hills were crowned with green mounds, and on some were standing stones, pointing upwards like jagged teeth out of green gums.
_{The Fellowship of the Ring - Book 1, Chapter 8: Fog on the Barrow Downs}

Their other mention, in History of Middle-earth, Volume VI: The Return of the Shadow, also doesn't give us any description of the stones, except that they may earlier have been known as "dark stones"

“At Rivendell sleeping Bilbo Gandalf. Some explanations. Ringmail of Bingo in barrow and the dark rocks - (the 3 hobbits had dashed past the rocks when suddenly they all became [? shut] off??) Gandalf had sent the water down with Elrond's permission.
Gandalf astonished to hear about Tom.

[...]

If the 'dark rocks' are the 'two huge standing stones' through which Bingo/Frodo passed in the fog on the Downs (FR p. 150) - they are called 'standing rocks' in the first version - it is odd that discussion of this was postponed till the hobbits reached Rivendell; but possibly the words 'some explanations' imply that Gandalf was able to throw light on what had happened.”
_{History of Middle-earth - Volume VI, The Return of the Shadow: The First Phase, Chapter 7: The Barrow-Wight}

Note: The "Dark Rocks" are not mentioned elsewhere in The Return of the Shadow, neither are "standing rocks"

This leaves us to speculate about the stones. Some people have speculated that they may have been some sort of "magical gateway" which marked the end of the Barrow Downs for the traveller, and that passing through means you're safe. This speculation comes around from Frodo passing through the gates and seemingly being safe, until he notices he lost his friends and returns. Only upon his return do the voices begin to sound, and he get captured.

Fear took him, and he ran back past the stones shouting wildly: ‘Sam! Sam! Merry! Pippin!’ The pony bolted into the mist and vanished. From some way off, or so it seemed, he thought he heard a cry: ‘Hoy! Frodo! Hoy!’ It was away eastward, on his left as he stood under the great stones, staring and straining into the gloom
_{The Fellowship of the Ring - Book 1, Chapter 8: Fog on the Barrow Downs}

Other speculate that it was a gateway into a barrow, as the horse reared after walking through and the darkness fell around him.

He had passed between them almost before he was aware: and even as he did so darkness seemed to fall round him. His pony reared and snorted, and he fell off.
_ibid.