This isn't the first time this has happened. When A Feast for Crows was published in 2005 and Martin (highly erroneously) announced that A Dance with Dragons would follow a year later, Amazon.com put a placeholder date for the latter book as 2008. The idea was that the publisher would unveil the real date and they'd bring the date up to the correct one. They weren't expecting the book to be that late and forgot to change it, resulting in confusion and then anger in less net-savvy fans when 2008 came and went without the book being released. Responding to fan anger and complaints from the publishers Amazon changed the release date...to 2032, suggesting either a great sense of humour or perhaps going overboard on contingency planning (the book was eventually released in 2011).
These issues could be avoided if Amazon could have simply put a "TBC" release date on books, but for some reason back then they couldn't. Learning their lesson, neither Amazon US nor UK has a page for The Winds of Winter at all. Obviously Amazon France hasn't learned from their example.
At this point it may be of value to look into why it takes such an immense amount of time for Martin to write these novels.
What the manuscript of A Dance with Dragons looked like in its raw form, all 1,520 A4 pages of it.
These are big books
The average novel, when we consider all genres, is between 80,000 and 100,000 words in length (which translates to roughly 300-350 pages in paperback, depending on formatting) and takes about a year to write. Science fiction and fantasy novels are usually longer, with 200,000 words (600-700 pages in paperback) taking two to three years not being unusual. The shortest novel in A Song of Ice and Fire is 300,000 words long with the longest - A Storm of Swords and A Dance with Dragons - both being around 420,000 words each. Those novels come in at well north of 1,200 pages in paperback.
Obviously some writers can churn out big books very quickly: Brandon Sanderson writes his Stormlight Archive novels (which clock in at around 400,000 words exactly) in three to three and a half years each, Peter F. Hamilton produced the 450,000-word The Naked God in two years and Steven Erikson produced 3,116,000 words of The Malazan Book of the Fallen (not including the first novel, which he wrote many years earlier) in just over eleven years, averaging 283,000 words a year during that time. On the flipside some authors are considerably slower: Suzanna Clarke took ten years to write the 308,931 words of Jonathan Strange and Mr. Norell and J.R.R. Tolkien took ten years to write the 455,125 words of The Lord of the Rings (and, arguably, sixty years to produce the 130,000 words of The Silmarillion, although that was only a summary of the much greater amount of work he produced in that time).
Writing without an outline can result in marvellously naturalistic and unforced character arcs and plot turns. On the other hand, it can also result in...less serendipitous writing events.
They are not written in a linear fashion
Martin's writing process is non-linear and unplanned. He writes several chapters in a row from one character, switches to another, writes several chapters from them, switches to a third and so on. At certain points he'll switch back to a previously-written character, but will then realise that new story points he has created elsewhere will now require a thorough rewriting of previously-drafted chapters to reflect these changes. As the novel continues and gets larger, this butterfly effect can be considerable: a late plot decision executed in what ends up as Chapter 48 may entail the complete page-one rewrite of Chapters 3, 6 and 12, the partial rewriting of Chapters 18, 23 and 32, and the re-ordering of several other chapters.
The writing process for A Song of Ice and Fire bears more than a passing similarity to chaos theory. However, it is not unprecedented. J.R.R. Tolkien executed The Lord of the Rings in a similar fashion, describing it as "waves coming up the beach...each time the waves reach a little higher" after rewriting the opening four or five chapters of the novel at least four times to accommodate tonal changes (from something closer to The Hobbit to something darker) and character shifts (from using Bilbo's son "Bingo" as the protagonist to junking him and bringing in a new character called "Frodo").
Martin's non-linear writing style has been criticised and it has been suggested that he employ an outline. However, Martin has famously said that he distrusts outlines, feeling that they sap the narrative energy from writing. Stephen King, Tolkien and Robert Jordan have also disdained outlines and produced, between them, several of the biggest-selling, popular and enduring works of fantasy ever written, so he may be onto something.
That said, Robert Jordan did produce an outline whilst planning the final Wheel of Time novel to help focus him on bringing the story to a conclusion (which proved tragically beneficial when he was later diagnosed with a fatal blood disease), indicating that other fantasy authors have seen some value in changing up even their long-standing writing habits to increase writing efficiency and speed as their series reaches the wrapping-up phase.
In addition, Stephen King once experimented with using an outline in response to fan criticism that his improvised writing style often resulted in subpar endings. The result was The Dead Zone, a reasonably well-regarded book which has been adapted for the screen twice. However, King said he hated the experience and has never used an outline again.
George writing on The Machine.
Martin's computer is steam-powered
Okay, it isn't. But it is pretty old. George R.R. Martin writes his novels on WordStar 4.0, a word processing programme released in 1987. The PC he uses is of similar vintage. WordStar is a non-WYSIWYG (What You See Is What You Get) programme, like Microsoft Word, and requires the author to move around the cursor using the keyboard and enter lines of code to enact formatting such as bold or italics.
Martin has used this stuff to write all of his short stories and novels on since the late 1980s and is at this point institutionalised to its use. Still, although it's perhaps a little more labour-intensive to use such a system it's not that much slower. It's still a way of getting words on the screen. What might be a bit more work is outputting the chapters in a format that can be emailed so George's editor can read them on her more up-to-date computer in New York City. And of course there's what happens when a 30+ year old computer stops working, as happened during the writing of A Feast for Crows: a legacy PC engineer named Stephen Boucher saved the day and the novel was dedicated to him.
Update: At some point in the recent past, Martin stopped using his old 1980s vintage machine and switched to a modern PC running WordStar 4.0 in a DOS emulator.
Writing white-on-black is something that would drive me crazy, making me want to murder every single character I was writing...wait a sec.
To summarise, Martin's writing style does not permit easy estimations of when he will be finished, especially given the heavy overlap where chapters are moved from the end of one book into the start of the next. Given the numerous missed dates on A Dance with Dragons and the resulting insane levels of vitriol, Martin has decided not to issue any predictions for Winter at all. He's also, unlike during his work on Dragons, not issued any page or word counts, perhaps feeling that this could also be misleading and people would be reaching all sorts of wrong conclusions.
The Winds of Winter is not done as of today. Martin and his publishers will confirm when it is, and when the book will be published. Based on precedent, this will be between 3 and 5 months after its completion is confirmed.