Does The Ice Dragon take place in the same world as A Song of Ice and Fire?

Question

Before he started A Song of Ice and Fire, George R.R. Martin wrote a children's book involving both fire dragons and ice dragons, called The Ice Dragon. It also features a fear of winter.

It is often said to take place in the same world as A Song of Ice and Fire, for instance in a review in The Guardian:

Game of Thrones author, best known for the bloody adult saga, reissues The Ice Dragon – a story for young readers set in the same world

But is it, and if so, when?

Answer 1

George R.R. Martin has said it is not set in the same world.

noybusiness: Is The Ice Dragon in the world of A Song of Ice and Fire like the back cover of it says?
grrm: No, it is not. The world of Ice & Fire did not exist when I wrote THE ICE DRAGON.

But as the follow-up question indicates, there is still some wiggle room for it to be retconned into the same world.

noybusiness: So it's not a retroactive "nothing's stopping it from being in that world (in one of the legendary historical ages of winter) if we want to imagine it is, but nothing mandates it is if we don't" ambiguous thing, then?

...which GRRM has left unanswered.

Answer 2

The other answer has shown the directly George denies the connection, but ice dragons do (might) exist in Planetos...

Of all the queer and fabulous denizens of the Shivering Sea, however, the greatest are the ice dragons. These colossal beasts, many times larger than the dragons of Valyria, are said to be made of living ice, with eyes of pale blue crystal and vast translucent wings through which the moon and stars can be glimpsed as they wheel across the sky. Whereas common dragons (if any dragon can truly be said to be common) breathe flame, ice dragons supposedly breathe cold, a chill so terrible that it can freeze a man solid in half a heartbeat.

Sailors from half a hundred nations have glimpsed these great beasts over the centuries, so mayhaps there is some truth behind the tales. Archmaester Margate has suggested that many legends of the north—freezing mists, ice ships, Cannibal Bay, and the like—can be explained as distorted reports of ice-dragon activity. Though an amusing notion, and not without a certain elegance, this remains the purest conjecture. As ice dragons supposedly melt when slain, no actual proof of their existence has ever been found.

_{The World of Ice and Fire - Beyond the Free Cities: The Shivering Sea}

George also a series of short stories set in what is known as "The Thousand Worlds". So while he says the two works are not the same world, they still might be connected... Alas, he has shot down this theory too...

[Q:] Asimov and Heinlein, late in life, both seemed to feel the urge to merge all of their books and stories into one huge continuity.

[A:] So far I do not feel the urge. No, Westeros is not one of the Thousand Worlds.

_{Not a Blog, "Last Year (Writing, Editing, Producing)"}

So I guess we have to accept that at most the ice dragons in A Song of Ice and Fire are a homage to The Ice Dragon.