When Alysanne Targaryen attempted to fly past The Wall on her dragon Silverwing, Silverwing refused to do so. Alysanne tried to do so three times, only to be denied each and every time.
“Thrice I flew Silverwing high above Castle Black, and thrice I tried to take her north beyond the Wall, but every time she veered back south again and refused to go. Never before has she refused to take me where I wished to go. I laughed about it when I came down again, so the black brothers would not realize anything was amiss, but it troubled me then and it troubles me still.”Fire & Blood, "Jaehaerys and Alysanne - Their Triumphs and Tragedies"
That...is pretty strange. Why would dragons, beings of fire, fear to fly past The Wall? Just so y'all know, ice is weak against fire. Fire melts ice, and dragonfire is capable of destroying castles. Just ask Harren the Black, who thought the mighty castle Harrenhal could withstand assault from Balerion, the mount of Aegon Targaryen. Suffice to say, he was wrong - and Harrenhal henceforth became a ruin.
Also, one quick point - unlike the show, the Others are not immune to fire. On the contrary, the Others also seem to be weak against fire - and normal fire at that (to say nothing of dragonfire):
Fire will dismay them, though, and they are vulnerable to obsidian... (AFFC 65)
Yep. It's safe to say if the Others encountered a dragon, they'd get melted like the visions in Dany's dream. Unlike the show, the Others are not immune to even normal fire - forget dragon fire.
That night she dreamt she was Rhaegar*, riding to the* Trident*. But she was mounted on a* dragon*, not a horse. When she saw the* Usurper*’s rebel host across the river* they were armored all in ice*, but she* bathed them in dragonfire and they melted away like dew and turned the Trident into a torrent*. Some small part of her knew that she was dreaming, but another part exulted. This is how it was meant to be. The other was a nightmare, and I have only now awakened. (ASOS 23)*
Based on all this, it's safe to say two things. One, dragons don't like the idea of going beyond The Wall for some reason (again, unlike the show, where Dany's dragons managed to cross over). Two, the Others are ''dismayed'' by normal fire and would likely be annihilated by dragon fire.
How does this make sense? If dragons are beings of fire and beings of frost hate fire - and dragons are plenty brave enough when it comes to fighting equally large or even larger dragons - why on earth would they have to fear the Others? It is clear the Others don't like fire, but what about the dragons?
It's not even an issue concerning fire magic in general, either. Melisandre was able to shoot down a warg on the other side of The Wall with fire magic just fine. She even admits she did it.
“… You had put the wildlings to flight, and the skinchanger Mance had left to guard his queen went mad when the eagle burned.” Jon looked at Melisandre. “Some say that was your doing.”
She smiled, her long copper hair tumbling across her face. “The Lord of Light has fiery talons, Jon Snow.” - ASOS
And here's this below. Varamyr Sixskins, the warg, acknowledges he was burnt alive.
His last death had been by fire. I burned. At first, in his confusion, he thought some archer on the Wall had pierced him with a flaming arrow… but the fire had been inside him, consuming him. And the pain…—- A Dance with Dragons
Melisandre even states her powers are stronger at The Wall.
The carved chest that she had brought across the narrow sea was more than three-quarters empty now. And while Melisandre had the knowledge to make more powders, she lacked many rare ingredients. My spells should suffice. She was stronger at the Wall, stronger even than in Asshai. Her every word and gesture was more potent, and she could do things that she had never done before. Such shadows as I bring forth here will be terrible, and no creature of the dark will stand before them*. With such sorceries at her command, she should soon have no more need of the feeble tricks of alchemists and pyromancers. - ADWD*
It's clear The Wall isn't weakening or anti-fire magic or something, as some have suspected. On the contrary, magical elements grow STRONGER at The Wall. This makes sense, it is considered one of the ''hinges'' of the world and there's no proof fire should get weaker here. So why could the dragons not cross? If Melisandre gets stronger at The Wall, why do dragons - magical beings of fire far stronger than Melisandre (she is trying to revive a dragon to help Stannis, after all) - shy away?
We know The Wall has some protective charms on it, strong spells that prevent the Others from supposedly crossing over to the realms of humanity. Said spells also prevented Coldhands, who seems to be an intelligent wight (this guy is quite a mystery), from crossing The Wall as normal people would.
"Why didn't he come with you?" Meera gestured toward Gilly and her babe. "They came with you, why not him? Why didn't you bring him through this Black Gate too?"
"He... he can't."
"The Wall. The Wall is more than just ice and stone, he said. There are spells woven into it... old ones, and strong. He cannot pass beyond the Wall*." - ASOS*
And it's not the only building of its kind.
"There was no need," she said. "He was unprotected. But here ... this Storm's End is an old place. There are spells woven into the stones. Dark walls that no shadow can pass—ancient, forgotten, yet still in place*."*
Ancient spells in the very stones of Storm's End, perhaps put there by its builder? Even if you don't trust Coldhands for some reason about The Wall (completely understandable), Melisandre seems a lot more trustworthy (she is a POV character, after all - and dishonesty isn't one of her main traits).
So at least we know it's possible. The Wall even has a ''talking gate'', the Black Gate, which Stannis describes as a ''magic gate'' IIRC. I think one thing's for certain: there's protective magic involved.
"Who are you?" the door asked, and the well whispered, "Who-who-who-who-who-who-who."
"I am the sword in the darkness," Samwell Tarly said. "I am the watcher on the walls. I am the fire that burns against the cold, the light that brings the dawn, the horn that wakes the sleepers. I am the shield that guards the realms of men."
"Then pass," the door said. Its lips opened, wide and wider and wider still, until nothing at all remained but a great gaping mouth in a ring of wrinkles. Sam stepped aside and waved Jojen through ahead of him. Summer followed, sniffing as he went, and then it was Bran's turn. Hodor ducked, but not low enough. The door's upper lip brushed softly against the top of Bran's head, and a drop of water fell on him and ran slowly down his nose. It was strangely warm, and salty as a tear.
Straight up one of the weirdest moments in ASOIAF. A door just talks, and...that's it? Unbelievable.
At any rate, it's safe to say The Wall is indeed a magical location, and that The Wall itself has magic built into it too. It might be safe to say The Wall really does deter the Others from crossing across (the Others are hostile to humans as we have seen so far and if they could get past it to kill some Watchmen, they would), but I'd argue one thing is even safer to say - to the point it may as well be officially confirmed. The Wall isn't just there to protect the realms of human from Others.
The Wall is also there to protect the Others from dragons - their worst and greatest enemy.
It's safe to say whoever built The Wall deliberately planned to make sure it would keep the Others safe from dragonfire, in addition to all the other spells they put on it. But who would do such a thing?
But why would Brandon the Builder - purported builder of The Wall (and Storm's End) alongside the Children of the Forest - build The Wall to protect Others from dragonfire, when The Wall is supposed to protect humanity from the Others?
If the Others are the enemy, wouldn't it make sense to NOT enchant The Wall in a way that prevents dragons from flying across and nuking them if necessary? Why didn't Azor Ahai, the Last Hero, Prince that was Promised, etc... not just exterminate the Others? They're just prettier orcs but more evil and deadly, from the looks of things. Why didn't humanity and the Children just finish them off for good? And why is dragonfire relevant in this scenario in the first place? Does Brandon the Builder and his Children allies know, from experience, that dragons are a mortal danger to the Others?
Were dragons used to fight the Others? All of that - and more - shall hopefully be discussed in another thread.
TLDR: 1) The Others dislike fire and it is quite likely dragon fire would finish them off.
2) The Wall allegedly protects humanity from the Others and definitively protects the Others from dragons flying through (though not all fire magic, as Melisandre proved).
3) The Wall is absolutely magical, and it's one of multiple magical buildings in ASOIAF. Storm's End is another.