The Ice Dragon is a children's book by George R. R. Martin, about a girl born during the long winter. The universe shows some similarities to the main universe of ASOIAF, but is it the same universe?
No, it is not.
Someone asked the author this question on his LiveJournal page, and for once he gave a straight answer:
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.
It's not in the same universe. Take it from the author himself, answering the same question in the comment section of his blog.
No, it is not. The world of Ice & Fire did not exist when I wrote THE ICE DRAGON.
The two other answers have 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.
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.