The empty sands of Sennen Cove sweep invitingly before us – the pristine beach shaded by a spectacular headland at the southwesterly tip of England. It’s a breathtaking spot for a day by the sea. Then the sun breaks through and the whoops of children surfing in the waves add to the atmosphere. The hardcore wetsuited family are the only people in sight, as the temperature remains stubbornly close to zero, with added windchill factor.

It is the first week in January, and we have come for a holiday to the rugged coast of Cornwall. You might ask why. The county is not known for winter holidays, with most tourists and second-home owners descending in their droves during the summer months, cramming themselves into all available cottages and campsites. But holidaying at this time of year offers the kind of peace that we long for after the excesses of December.

And that’s the mindset we travel with, packing enough Christmas toys, games and books to make the most of any enforced downtime, but with the usual beach apparatus, wellies and an enthusiasm for brisk walks that will ensure we don’t waste our time on the stunning coastline.

For the first couple of days, we book into The Old Coastguard, a beautifully renovated Victorian hotel jutting out on the rocks of Mousehole fishing village. We have the family room up in the gods, painted in sunshine yellow with Aztec-style carpet runners and blue-hued furnishings. The room’s bright decor contrasts with the stormy weather, but – unlike in the summer months, where a rainy day can spoil carefully laid plans – we embrace the cosiness of the hotel, throw ourselves at the local arcade and let the children alternate between playing with their remote-control cars on empty beaches and turning their adjoining bedroom into a nightclub with the bedside radio.

We have plenty of peaceful moments to take in the view from the window seat. As the light begins to fade into a grey, stormy expanse outside, we head down into the hotel’s dining room, the roaring fire welcoming us into the long, gloomy night that lies ahead.

There are enough guests extending their New Year’s Eve break to make for a pleasant atmosphere, without the elbow-sharpened hustle that can sometimes dictate summer holiday evening meals in busy venues. We load up on plates of fresh hake and a bavette tartare, before wrapping up and heading out into the night to have a look at the popular Christmas lights in the harbour. Others are doing the same, stopping to admire the large cat or the sea monster peeking out of the water, before ascending up into the village along its steep paths to complete the tour.

Next is a drive on quiet roads to Cove Cottage, overlooking the sugary sands of Sennen Cove. It is during this part of the break, with what feels like one of the UK’s best beaches to ourselves, when the rain backs off and we can really lean into the crisp, clear days.

We join an organised beach clean – all four of us learning how to spot and remove microplastics in the engaging company of Emily Stevenson and her father, Rob, who together founded Beach Guardian. It is impossible to think, as we look across the clear expanse of Sennen beach that we will find any rubbish but, to the children’s delight, we fill buckets with multi-coloured treasure.

There’s stunning local artwork and sculpture to enjoy and we spend a few hours, without the typical summer hustle, perusing galleries in St Just. Rather than shuffle shoulder to shoulder through the packed shops of St Ives on a sticky July afternoon, we idle through the Tate Gallery and Barbara Hepworth Museum. As we exit the Tate, we look down on a row of surfers silently bobbing up and down, immune to the drizzle.

One of the themes we keep coming back to on this winter break is being able to support local business and hospitality out of season, and whether it will help their viability all year round. To that point, a final Friday evening meal before the long journey back north sees us return to Mousehole and the seafood restaurant 2 Fore Street. Knowledgable, friendly staff help us navigate a sublime menu with appropriate wine choices and, by the time we finish our first course of shell-roasted scallops thermidor with pangrattato and crab soup with parmesan toast and rouille, the restaurant is full. It’s not far past 6pm but it’s already dark outside, the streets are black, wet and quiet. Inside, however, there’s a vibrant atmosphere with the flow of weekend chatter and it could have been an August bank holiday.

We’d come to enjoy wrapping up in woolly hats and scarves and heading out into the bracing weather. Rather than feeling bereft at the lack of warmth, there is something pleasurable about embracing the elements and seeing a different side to a seaside resort out of season.

• Nazia Parveen travelled courtesy of the Experience Project, a €2.8m project co-funded by the European Regional Development Fund and Cornwall Council to develop a sustainable cultural tourism model by extending the tourism season