I have never been so grateful for a thermos of tea in my entire life. There we were, trundling up the coast of North Zealand in mid-January, the windscreen wipers working overtime against what the Danes cheerfully call "typical winter weather," and my partner suddenly announced that the booking confirmation was on his phone. His other phone. The one currently sitting on our kitchen table in Crouch End.

This is how we arrived at Gilleleje Strand: slightly damp, thoroughly dishevelled, and relying entirely on my increasingly unreliable memory of a booking reference number I had skimmed three months prior during a bout of optimistic summer planning. The woman at the key collection point took pity on us, or perhaps simply wanted us out of her warm office before we dripped on everything. Either way, she handed over the keys with the kind of smile that suggested she had seen worse.

The drive from the little harbour town of Gilleleje itself took all of four minutes, winding past closed-up summer houses that huddled together like seabirds against the grey. You could tell this was a place that woke up properly in June. The paintwork on the neighbouring cottages looked fresh enough, but the gardens were sleeping, the barbecues were tarpaulined, and not a single Danish flag fluttered from its pole. It felt like we were arriving at a party the morning after, except the party had been in July and we were very much late.

Then we opened the door to our holiday home, and I understood immediately why people bother with off-season Denmark. The place smelled of pine and salt and something else I could not place until my partner identified it as "a working radiator." Bliss. The living area was all pale wood and big windows, and through them stretched the Oresund, moody and magnificent, the Swedish coast just visible through curtains of winter rain. In summer, I imagine, you would throw open those doors and never close them. In January, we stood there in our coats, steaming slightly, watching a container ship inch its way towards Helsingor and feeling rather pleased with ourselves.

The kitchen had clearly been designed by someone who actually cooks on holiday, not merely assembles cheese boards. We unpacked our emergency supplies - the tea, some rather squished crumpets, a block of cheddar that had seen better days - and I caught myself doing that thing I always do on arrival: opening every cupboard and drawer with the enthusiasm of a burglar, as if the previous guests might have left behind something fascinating. They had not, unless you count a comprehensive collection of Tupperware lids without matching bases, which I do not.

That first evening, we walked down to the shingle beach proper, the wind finding every gap in our inadequate jackets. The light was doing extraordinary things, breaking through clouds in pale gold shafts that turned the freezing water silver. A lone fisherman stood at the water's edge, utterly immobile, apparently unconcerned that his extremities must surely be turning blue. We nodded at each other, that brief solidarity of people who have chosen to be outside when sensible folk are indoors.

Back at the house, we cranked up the heating, opened the wine we had sensibly packed, and watched the darkness swallow the sea entirely. Somewhere out there, Copenhagen glittered, only an hour away but feeling like another country in this hunkered-down season. I thought about how different this would be in July: the long luminous evenings, the children shrieking in the water, the smell of grilling fish from the harbour restaurants. I would love that too, no question. But there was something about this stripped-back winter version that felt like a secret, like we had been let in on something not everyone bothered to discover.

The tea, by the way, was excellent. Even the second mug, which I made after we found the proper mugs in the cupboard above the fridge, the one I had somehow missed during my initial raid. Some things, I reflected, are worth the wait.