The Patriot Centre at George Mason University, half an hour west of Washington, is a popular place to watch concerts, college athletics, professional wrestling and other events that command the attention of the adult world. But no event in the 29-year history of the arena has attracted as many people or earnt as much money as October's performances of "Disney on Ice Presents Frozen". For six days, waves of little blue-and-white Princess Elsas – and quite a few costumed parents – sang the movie's hit song "Let it Go" at the top of their lungs, enjoyed £10 snow cones (syrup-soaked ice shavings), posed for £15 pictures with cardboard cut-outs, and waved plastic sticks, which had miraculously become £18 magic wands.

Behold the bewitching power of branding. In the year since Disney's latest princess movie, Frozen, opened last November, Elsa and her sister Anna have rapidly become two of the world's most successful product endorsers. Disney said earlier this month that it had already sold three million Frozen dresses in North America, which, as it happens, is roughly the number of four-year-old girls in North America. In January, Frozen wedding dresses go on sale for £750. Next summer, Adventures by Disney is offering tours of Norwegian sites that inspired the film's animators, at prices starting north of £3,200. The company is also rolling out Frozen-branded "apples and grapes, juice, yoghurt, bandages and a complete oral-care line". Disney estimates that Frozen has brought in around £65m in retail revenue over the past year. The company's chief executive, Robert A Iger, told CNBC that he expected holiday sales to be "very, very hot".

The creators of Frozen, Jennifer Lee and Chris Buck, tell me that they set out to create characters young girls would recognise. "I love Cinderella," Lee says. "Am I anything like her? No. I grew up and became someone more independent." Elsa and Anna, she says, "are princesses because they've got the weight of a kingdom on their shoulders, not as the solution to a happy ending".

Lee and Buck realised they had succeeded, and then some, soon after the movie was released, when they went to see it like ordinary people. Lee found herself in a New York cinema where many audience members already knew the words. Then she started to hear people singing on the street. A year later, they haven't stopped. Does she ever get tired of hearing "Let it Go"? No. Not really. Not yet. "When I'm old, it will be the only thing left in my brain," she says.

Frozen: The Princess Diary Show all 7 1 /7 Frozen: The Princess Diary Frozen: The Princess Diary Frozen: The Princess Diary Princess Bay sits proudly upon her throne Frozen: The Princess Diary Frozen: The Princess Diary Bay enjoying her big day out Frozen: The Princess Diary Frozen: The Princess Diary Debi, Fairy Godmother in Training, applies the finishing touches Frozen: The Princess Diary Frozen: The Princess Diary Cold comfort: ‘Frozen’ has been a huge success both on and off the screen Disney Frozen: The Princess Diary Frozen: The Princess Diary 'Frozen' merchandise in Japan (Rex) Rex Features Frozen: The Princess Diary Frozen: The Princess Diary Olaf, the slapstick snowman, is one of many beloved 'Frozen' characters Disney Frozen: The Princess Diary Frozen: The Princess Diary Princess Elsa from 'Frozen'

Brands are said to be in decline. Studies show that customers are less loyal to companies, quicker to try something new. Products increasingly rise and fall on their own merits. "Brand names have become less important as proxies for quality," says Itamar Simonson, a professor at Stanford University. He argues that consumers now get better information about products from the internet. But Disney, perhaps more than any other large company, appears to be impervious to the trend. It helps that the company is not selling products based on the quality of craftsmanship but on the quality of its stories. Disney also specialises in selling affordable luxuries. An Elsa dress is considerably more expensive than an ordinary dress, like a cup of Starbucks coffee costs more than an ordinary cup of coffee. But it is not that expensive. Every item of the dozens of Frozen products at the Disney store costs less than £65. More important, though, to Disney's success is that many of its best customers are still learning how to read and don't care what things cost. It's not as if toddlers check out Amazon reviews.

As a result, Disney is in the midst of a golden age of profitability. Disney characters have been endorsing products since 1929, when Walt Disney put Mickey Mouse on a writing tablet. But licensing, which began as a sideline, has become the main event. In most years, Disney makes more money from selling branded movie merchandise than from the actual movies. "We create products that extend the storytelling – the emotional connection that the consumer has when they're seeing the film carries on in the three-dimensional world," says Josh Silverman, the executive vice-president for global licensing. A recent favourite, he says, is the Olaf snow-cone maker. Modelled on the slapstick snowman who provides the comic relief in Frozen, it emits frosty treats from a somewhat disturbing hole in its belly.

The popularity of Frozen is also buoyed by the expanding toy market for girls. Princesses may seem like a permanent feature of the toyscape, but they were less common before the 1990s. "The idea that pink princess fantasy dream dolls have always been a part of girlhood is false," says Elizabeth Sweet, a lecturer at the University of California, Davis who studies the cultural history of toys. Dr Sweet has found that the popularity of gender-neutral toys reached a peak in the mid-1970s. Since then, toymakers have embraced the market-doubling effect of pushing certain toys to boys and other toys to girls. Dr Sweet says the level of gender segregation has never been higher. A typical big-box store might have four aisles of blue toys and four aisles of pink toys with an aisle of yellow toys in between. "Separate but equal," she says. Lego, for example, evolved from simple packs of building blocks into play sets mostly sold to boys, often with brand tie-ins. In 2012, the company introduced Lego Friends, which is basically Lego for girls.

Disney really began to focus on princesses in 2000, after a new executive went to see a Disney on Ice show and was struck by how many of the girls in the audience were wearing home-made princess costumes. "They weren't even Disney products," the executive, Andy Mooney, told the writer Peggy Orenstein for her book about the rise of princesses, Cinderella Ate My Daughter. The Disney Princess line now makes about £2.5bn a year, on par with the earning power of Mickey Mouse himself. (The Frozen girls are not, as yet, official members of the Princess ensemble.)

This market has similarities with, of all things, the American pharmaceutical industry. Drugs are marketed to patients, who tend to trust brand names over generics, and are paid for by insurance companies under their contractual obligations. This has an inflationary effect on drug prices, leading to those eye-popping numbers that send uninsured Americans fleeing US pharmacies to try their luck in Tijuana. Similarly, toys and the like are marketed to children and purchased by parents. People who would never buy a £10 snow cone for themselves will buy one, gladly or grudgingly, for each of their children.

After all, who wants to say no to their princess?