Though a sequel to Frozen has been slow in coming - Frozen 2 is in cinemas later this week - it has been an absolute inevitability, ever since Frozen moved past The Lion King (1994) to become the most successful animated film of all time.

I was the father of a new baby girl when the Frozen madness began back in 2013. In the tiny gaps between ninja nappy-wrapping and sprinting out to the shops on emergency Persil runs, I was vaguely aware of the arrival of a cultural phenomenon.

I didn't know the specifics: nothing of the heroine-princess Elsa, her younger sister Anna, their gang of comic friends or their quest to save a frozen Scandinavian kingdom from ruin.

I hadn't heard any of the songs which, people said, were wilier and more mischievous than the straighter, soapier, we're-in-love-now ballads that defined Disney movies past.

My first exposure to the curious potency of Frozen's soundtrack came that first summer after its release. One of the tracks, For The First Time In Forever, caught my ear. I went away intrigued, though not expecting to find out much more about Frozen for at least another 15 years - at which age my daughter, having been raised on a diet of leather-bound Charles Dickens and bunraku mime, would be allowed to watch her first Hollywood film.

We trick ourselves any time we think we can curate a careful menu of things our kids will obsess over.

My daughter and I were days into a rained-off holiday in the countryside and the place had a DVD player, plus a copy of the film. What could it hurt?

I brought in snacks. Arranged cushions. We sat and watched the thing, and she surprised me, when the baddie did an embarrassing bad-guy dance, by gurgling out a laugh. Before long we had watched Frozen a second time, then a third. It became one of our things.

"Fer-zen," she called it.

Ten viewings, then 15. In these early innocent stages -mere foothills of a coming obsession - my daughter seemed to like the wacky supporting characters best: a brought-to-life snowman, Olaf, waddling about at waist height; a lonely mountain-man, Kristoff, who gets a little song about preferring his pet reindeer to people.

The film's final song features musical trolls who band together for a topsy-turvy dance number about learning to tolerate people's flaws. These trolls, I eventually noticed, somewhere around the 20th or 25th viewing, had been sneaked a cheeky line in which they speculated that Kristoff and his reindeer enjoyed a relationship "a little outside of nature's laws".

Of all the un-Disneyish subjects: bestiality. I must have gasped.

"What? What?" my daughter asked, while I winced and bit my tongue. Here was that flattering sense, well known to parent-chaperones at Pixar movies, of a gag aimed over the heads of the kids for the grown-ups.

As with a great many Disney movies, the plot of Frozen requires that the lead characters be orphans. In order to keep the plot brisk and economical, the parents die early in a shipwreck. This happens mid-song, their ship going down under a wave during a storm.

Watching through adult eyes, I always found this a deft piece of storytelling. It never occurred to me that my daughter had missed anything, not till our 45th or 50th viewing came to an end, with the winter-struck kingdom returned to sunshine and prosperity.

I asked my daughter, idly, what she thought would happen to the sisters next. She yawned, throwing out her lengthening limbs into a massive, contented, after-movie stretch. She said something about Elsa and Anna's parents finally getting home from their sea voyage.

Silence on the sofa. The credits rolled. "Oh, baby," I began. Deep breath. And so we had our first conversation about death.

My daughter turned six this year. One day she came to find me, with the air of someone who'd been sitting on a big confession for a while. Deep breath.

She admitted she'd started to find Frozen boring. Babyish. She would come and see the sequel with me - a concession to my feelings. But the fact was, she had other favourites. We hugged.

I thought of the time she first teetered away, walking, or spent a whole morning at nursery by herself - fantastic new beginnings that also marked, unequivocally, an end.

THE GUARDIAN

• Tom Lamont is a freelance writer.