Bone-chilling gusts whip through the lowlands and across the ice-choked straits. Everything in the wind's path—forests, villages, old castles and towers—is glazed in sheets of frost and snow. Hail pelts the cobblestone streets. Winter is coming, all right. One of the worst Nordic blizzards in decades is pummeling Copenhagen.

But Nikolaj Coster-Waldau, wearing jeans, a V-neck tee, and a hipster-ish leather string around his neck, couldn't be more chipper. He has just ordered something in Danish from a pretty young waitress, the only other person riding out the storm in this café on the edge of the Baltic Sea. After she hurries off, Coster-Waldau leans back in his chair and flashes a grin so wide and white it would make Tom Cruise text his dentist. "You know that thing they say about Danes? How we're the happiest people on earth?" he says with a contented chuckle. "It's because we have low expectations. Don't expect too much. You'll be pleasantly surprised."

And Coster-Waldau is surprised—very, very pleasantly—to find himself playing Jaime Lannister on Game of Thrones, HBO's darkly mystical, shockingly violent, hugely popular drama about the struggle to rule the kingdom of Westeros (think Lord of the Rings' Middle-earth, only with graphic violence, nudity, and incest). At 43, Coster-Waldau is no newcomer—he's had roles of varying sizes in more than 30 films (including last year's Oblivion, opposite Tom Cruise, and Mama, opposite Jessica Chastain) and even landed a series, Fox's short-lived New Amsterdam. But he's never been in anything like Thrones—few actors have.

In an era when TV shows are considered successful if they can bring in a million viewers, Thrones, which begins its fourth season this month, has been drawing as many as 13.6 million an episode, second only to The Sopranos in HBO history—for now. More than a hit, though, it's the rare TV series that transcends the bounds—and fan base—of its genre, attracting an audience from all across the spectrum, permeating the whole pop culture. On Sunday nights, Thrones fans light up the Twittersphere with impassioned commentary about the drama's hairpin plot twists. On Monday mornings, it's Topic A in offices across the nation—even the Oval one: It's one of President Obama's favorite shows.

"Yeah, it's crazy," acknowledges Coster-Waldau, in an accent so subtle it's nearly imperceptible (although "crazy" comes out "creh-zee"). "There are some very intense fans. We did a premiere last year in Seattle, and I got a taste of it. It was a little claustrophobic. All these people wanting to take a picture with me. One guy was like, 'Do you mind if I take a picture of your shoe? I have a thing with shoes . . .'"

It is indeed crazy. Game of Thrones' sprawling cast—a terrarium of international talent headlined by Peter Dinklage and Lena Headey, along with hot young things like Emilia Clarke and Kit Harington and scads of faces familiar to Masterpiece Theatre viewers—has numerous candidates for footwear photography, all playing characters more likable than Coster-Waldau's. On paper, Jaime Lannister—a rakish, brazen, vain, egotistical cold-blooded killer who sleeps with his sister, a guy who didn't think twice about pushing a 10-year-old out a castle window, who spent a good chunk of last season being held prisoner, beaten, spit on, and covered in filth and having his hand chopped off—is an all-but-impossible vehicle through which to launch a career as a leading man.

Still, Coster-Waldau is giving it the old Danish try. He's positioning himself for a big Hollywood push, ticking off all the right boxes. Big-studio romantic comedy? Check. He spent last summer making The Other Woman with Cameron Diaz, which opens this month, playing a caddish husband carrying on multiple affairs. Fantasy-adventure film with franchise potential? Check. This summer, he'll be shooting Gods of Egypt, a 300-esque epic costarring Gerard Butler. Scandinavian art-house flick with critical appeal? Tjek. He's currently filming the drama A Second Chance, directed by the Danish cinema darling Susanne Bier.

"Oh, Nikolaj is totally a leading man," Diaz says of her costar. "Men aspire to be like him, which is the one thing all the leading men I've known have in common. Women aspire to, well, find a man like him." Plus, she adds, "he's really good-looking."