Before my job as a theatre journalist, I happened to spend a week or so in Croatia as a press photographer during the war years in the 1990s. Among my strongest memories are of Paddy Ashdown striding passed shell-shocked Bosnian refugees on his way to a meeting to promote peace. But I also remember the feel of a country that, like much of the region, was in the grip of nationalism. It left a sour taste. And now even Serb or Croat football crowds seem to me to have a fervour that chills to the bone.

This National Theatre debut by UK-based Croatian writer Tena Štivicic puts much of that national character in context. Although I suspect the play would have a greater impact in Croatia's national theatre than it does at ours. It's a bit of behemoth in terms of scope and ambition. The eponymous three winters belong to the years 1945, 1990 and 2011; and the action, set in the Kos family's grand Zagreb house, lurches back and forth between all three.

The years represent three crucial moments of Croatian and European history: when the Communists replaced the Nazis at the end of the Second World War; when Yugoslavia split into its national parts and, perhaps less dramatically, when Croatia became committed to joining the EU.

These events are viewed through three generations of the mainly female Kos family whose Communist forbear Rose (Jo Herbert) took possession of the house – or one large floor of it – when its Nazi-sympathising aristocratic owners fled to South America. One of them, it emerges, has stayed behind.

The later occupants have a sense of entitlement to the building because Rose's mother Monika (Josie walker) was a housekeeper to the former owners who mistreated her. And, as different generations of the Kos family adjust to the realities of life after war in 1945 and before war in 1990, the question of entitlement to the house in which they live hangs like a shadow.

Štivicic is deeply interested in the choices made by her countrymen at these crucial junctures history, right up to the 21st century. Howard Davies's imperious production deals with a lot of events in the years between by projecting news footage on to the walls of Tim Hatley's elegant set.

During Nicholas Hytner's reign at the National, Davies has become the National's go-to director for sumptuous revivals of Chekhov, Bulgakov and Gorky, so its hard not to see this new play as the latest in a series that grapples with east and central European history.

Yet Štivicic is no Russian master. There is very little about her protagonists that draws you into caring about their fate. They're not even likeable. They argue about politics but, apart from the character Alicia (Jodie McNee), who like Štivicic herself is based in the UK, there is always the sense that each family member is shadowed by shame for decisions they made in the past. In that sense, perhaps the play wouldn't go down so well in Croatia.

With one of the periods in which the play is set defined by a Nazi past, and another that presages civil war, moral ambiguity is hardly surprising. Where the play makes its mark, however, is in revealing the psychology of a country constantly grappling with the legacy of its conflicts and politics in ways that we just don't have to.

This is slow-burn drama but it builds to a gripping climax that reveals how ruthless, self-serving pragmatism has taken over from all other isms that have caused the country so much strife.