Like the well known Rosetta Stone, ASoIaF's blue winter roses help to decipher what otherwise might have been a mystery. In this case, Jon Snow's true identity as the son of Rhaegar Targaryen and Lyanna Stark.
Before we get to the analysis, there are a couple of issue I want to address. The first being what I consider to be the biggest misconception about blue roses, and the second on where I think they might be most useful in arguing R+L=J.
1) Probably the biggest misconception regarding the blue roses is that they symbolize Lyanna Stark. A belief which is no doubt encouraged by GRRM, and based on a kind of cognitive bias. Because every occurrence of blue roses in AGoT is accompanied by Lyanna. An arrangement which belies its own meaning. For it is not until Ned's final chapter that we learn where – and more importantly who – Lyanna's pale blue roses come from. Which segues into my next point.
2) Every now and then a debate will arise regarding the certainty of Jon's paternity, whilst conceding the maternity; i.e., ?+L=J. The answer to which is: follow the trail of blue roses. Chronologically, this leads back to the tourney at Harrenhal in 281AC, when Rhaegar Targaryen placed a crown of winter roses in Lyanna's lap. Not to state the obvious, but: in order to understand the recurring thoughts and visions of Lyanna with blue roses, it helps to start at the beginning. In other words, you should always remember that Rhaegar gave Lyanna her blue roses.
(A quick note regarding real world blue rose symbolism. "The meaning of the blue rose is about mystery [as in; who is Jon Snow's mother?] or attaining the impossible. The blue rose is also used as a symbol of love at first sight [R+L?]. The blue coloring also represents royal blood [which Jon receives from his father] so it can represent splendor and regal majesty.")
“I was with her when she died,” Ned reminded the king. “She wanted to come home, to rest beside Brandon and Father.” He could hear her still at times. Promise me, she had cried, in a room that smelled of blood and roses. Promise me, Ned. The fever had taken her strength and her voice had been faint as a whisper, but when he gave her his word, the fear had gone out of his sister’s eyes. Ned remembered the way she had smiled then, how tightly her fingers had clutched his as she gave up her hold on life, the rose petals spilling from her palm, dead and black. After that he remembered nothing. They had found him still holding her body, silent with grief. The little crannogman, Howland Reed, had taken her hand from his. Ned could recall none of it. “I bring her flowers when I can,” he said. “Lyanna was... fond of flowers.”
- Eddard I
As they came together in a rush of steel and shadow, he could hear Lyanna screaming. “Eddard!” she called. A storm of rose petals blew across a blood-streaked sky, as blue as the eyes of death.
Her eyes burned, green fire in the dusk, like the lioness that was her sigil. “The night of our wedding feast, the first time we shared a bed, he called me by your sister’s name. He was on top of me, in me, stinking of wine, and he whispered Lyanna. “
Ned Stark thought of pale blue roses, and for a moment he wanted to weep. “I do not know which of you I pity most.”
He was walking through the crypts beneath Winterfell, as he had walked a thousand times before. The Kings of Winter watched him pass with eyes of ice, and the direwolves at their feet turned their great stone heads and snarled. Last of all, he came to the tomb where his father slept, with Brandon and Lyanna beside him. “Promise me, Ned, “ Lyanna’s statue whispered. She wore a garland of pale blue roses, and her eyes wept blood.
Let's revisit The Moment When All the Smiles Died, from Eddard XV, because there is an addendum which belongs here, I think.
Ned remembered the moment when all the smiles died, when Prince Rhaegar Targaryen urged his horse past his own wife, the Dornish princess Elia Martell, to lay the queen of beauty’s laurel in Lyanna’s lap. He could see it still: a crown of winter roses, blue as frost.
Ned Stark reached out his hand to grasp the flowery crown, but beneath the pale blue petals the thorns lay hidden. He felt them clawing at his skin, sharp and cruel, saw the slow trickle of blood run down his fingers, and woke, trembling, in the dark.
Promise me, Ned, his sister had whispered from her bed of blood. She had loved the scent of winter roses.
But there were others with faces he had never known in life, faces he had seen only in stone. The slim, sad girl who wore a crown of pale blue roses and a white gown spattered with gore could only be Lyanna.
- Theon XI
A blue flower grew from a chink in a wall of ice, and filled the air with sweetness.
-Daenerys IV (HotU)
“A dead man in the prow of a ship, a blue rose, a banquet of blood… what does any of it mean, Khaleesi? A mummer’s dragon, you said. What is a mummer’s dragon, pray?”
- Daenerys V
Aside from affirming that the blue flower in the HotU was in fact a blue rose, the latter quote serves little other purpose, as far as I can tell, and is presented without additional comment.
“Not kind,” said Cersei, “merely truthful. Taena tells me that you are called the Blue Bard.”
“I am, Your Grace.” The singer’s boots were supple blue calfskin, his breeches fine blue wool. The tunic he wore was pale blue silk slashed with shiny blue satin. He had even gone so far as to dye his hair blue, in the Tyroshi fashion. Long and curly, it fell to his shoulders and smelled as if it had been washed in rosewater. From blue roses, no doubt. At least his teeth are white. They were good teeth, not the least bit crooked.
- Cersei IX
The Song O' the Winter Rose; Bael, Rhaegar, Mance, R+L=J:
Based on the parallels between Rhaegar and Mance (ASoS, Jon I), a few people believe that the latter is really the former in disguise, having somehow survived the Trident, changed his appearance, made his way to the Wall, concocted an entire back story for this new identity, etc., even though GRRM said: "Rhaegar was cremated, as is traditional for fallen Targaryens." - Link. So, it seems like a better explanation than M=R probably exists.
In ADwD, Mance suddenly seems to have lots of parallels with Bael the Bard. Rather than assuming this is because Mance is really Rhaegar, and Rhaegar is trying to follow in Bael's footsteps, I believe GRRM is actually reinforcing the connection between Rhaegar and Bael, via Mance. One that already existed because of the similarities between R+L=J and the song o' the winter rose.
At their core, both feature singers who stole Stark maidens and gave them sons. There are other similarities, for example, that Rhaegar was the crown prince, while Bael went on to become the King-Beyond-the-Wall.
I believe it is supposed to prompt anyone who doesn't already know about R+L=J to connect blue roses to Stark maidens and their sons. In other words, it's a clue that Jon has Stark blood through his mother, not his father; i.e., Jon is half-Stark, but Ned is not his father.
This is, of course, the BtB story as it pertains to R+L=J. There are almost certainly other events that are foreshadowed by that tale.
Thanks for reading.
Edited by J. Stargaryen, Today, 12:25 AM.