The cold never bothered them anyway.

On a chilly Thursday evening, 200 people jammed the sidewalks outside the St James Theater in New York, where the musical Frozen, the latest venture from Disney Theatrical Productions, had staged its first Broadway preview.

Frozen remains the highest-grossing animated movie of all time, making $1.2bn worldwide since its release in 2013. Very loosely based on the Hans Christian Andersen story The Snow Queen, it’s set in the fictional land of Arandelle and describes Princess Anna’s quest to find and redeem her older sister Elsa, a blond icemaker with a thing for statement gloves.

To adapt the film for Broadway, the original creative team – composers Kristen Anderson-Lopez and Robert Lopez and writer Jennifer Lee – reunited to shift scenes, lose a snow monster and add 12 new songs. One new number, Elsa’s ballad Monster, would be released that same night online, but several people came out humming another new tune, Hygge.

As the wind lashed 44th Street, attendees stood comparing merchandise – fluffy snowmen, fur-trimmed sweatshirts – and swallowing the last of pricy cerulean cocktails like the Heart of Arendelle. Not too many adult women had come in costume, but several had assembled blue and white outfits. One man proudly displayed his blue socks. Many tiny Elsas stood near the stage door, hoping for autographs, and a few Annas, too, even though it was hours past bedtime.

“It was really, really good,” one of the Annas, 10-year-old Molly Sarfert said. “There were some new songs, but they were really on it.” She even claimed to like the “hidden folk”, one of the musical’s innovations replacing the film’s trolls.

“You said they were creepy,” her mother Geri, 46, countered.

Development of the $25m to $30m musical, now directed by Michael Grandage and designed by Christopher Oram, was initially fraught, with the production cycling through two directors, two designers, three choreographers and cast changes, too. Reports from the pre-Broadway tryout in Denver were on the cheerful side of tepid.

The cast of Frozen at the end of the first night on Broadway. Photograph: Disney Theatrical Productions

Frozen, which stars Broadway regulars Caissie Levy and Patti Murin as inclement princesses, could flop, like Tarzan, but it could also go on to crush the Broadway box office, like The Lion King, which has earned nearly $8bn, or Aladdin, which continues to post strong profits. It will have some competition this spring from Harry Potter and the Cursed Child, which begins previews next month and should also appeal to family ticket-buyers.

But for several in the crowd, there was no competition at all. Dustin Overfield, 34, stood outside holding a huge bag of souvenirs and waiting for his wife. They’d flown out from Detroit to see the show. “It’s her Valentine’s Day present,” he said. He’s already pre-ordered the cast album and he proudly showed off a piece of sheet music signed by the composers.

Away from the stage door, other groups clustered. Adam Kaufman, 43, who had come with his fiancee and some friends, described the show as “amazing, totally magical”. His friends, who had bought sweatshirts, thought so too. A few of them were surprised by what Kaufman called “a number that was a little risqué”.

“There was more nudity than expected from Disney,” said his friend Jenn Mante, 36.

But everyone agreed that the reindeer, Sven, was an improvement on the movie, and so was the snowman, Olaf.

Half an hour later, the crowd still hadn’t dissipated. “Some people are worth melting for,” Olaf says. And some shows are worth shivering for.