Our shelter for the night is a simple wooden hut, 6,560ft above sea level. We’ve no electricity, scant phone signal, no wi-fi. The dim light of a log fire and a few candles casts spooky shadows on the walls around the decorative skulls of long-dead deer. A frog the size of a pigeon hops about outside the front door. What kind of night are we going to have? We arrived in San Cassiano two days before — me, my husband, John-Paul, and our daughter, Nancy (12) — having flown to Innsbruck then crossed the border into the Italian South Tyrol, then up, up, up into the jagged peaks of the Dolomites — snow-topped even in high summer but golden in the setting sun.

We planned an active holiday, with some luxurious relaxation built in, courtesy of Hotel & Spa Rosa Alpina, a five-star in San Cassiano that’s been run by the Pizzini family for generations. San Cassiano is best known for skiing (it has an impressive 80 miles of slopes) but in summer it offers us the chance to go hiking, climbing, and to enjoy high-end cooking lessons — not to mention spend many joyous hours flying about on cable-cars and chairlifts. On our first morning, the hotel’s mountain guide, Diego, takes us on a hike into the mountains. I’ve rarely seen a man as happy as the sprightly Diego, who almost skips as he walks. In his time, he’s guided many notable people through the hillside meadows — media moguls, presidents and now, er, us.

We’re here in mid-July: perfect to enjoy the mountains in full bloom with blues, pinks, yellows and whites; clover, forget-me-nots, primulas, orchids, globeflowers, mountain avens, indigo gentians. Many of them are edible, and Diego regularly dives into the tangle of vegetation to pull out tasty morsels of wild spinach, or garlic, or violas to eat. I’d been unsure about having a guide with us — worried Nancy might get bored with endless facts. But she’s entranced by Diego, and together they walk his beloved ‘pale mountains’ and hunt the wilderness for more things to eat. This being Italy, there’s always something tasty around the corner. After a short walk, we arrive at Bioch, a mountain refuge with stripy deckchairs to relax in as you gaze at glacier-topped Marmolada mountain in the distance.

We’re greeted by Markus, Bioch’s exuberant host, who wears Austrian-style lederhosen. His wife, Suzanne, is resplendent in a green dirndl. This is border country and Diego explains how the Austro-Hungarian Empire lost the South Tyrol to Italy after World War I. Everyone speaks German as well as Italian (plus Ladin, the local language). Much of the cuisine is Austrian but with an Italian twist (or is that Italian with an Austrian twist?). We tuck into hearty barley soup and tutres (crispy pancakes filled with spinach and ricotta or sauerkraut).

Bioch is part of the Giro d’ltalia dei Sapori, a culinary scheme involving 10 mountain huts in the Alta Badia ski area working with Michelin-starred chefs. Thus I find myself lunching on steamed Arctic char, infused with aromatic herbs — a dish created by Norbert Niederkofler, the head chef at Rosa Alpina’s two-Michelin-star Restaurant St Hubertus. Diego decides Nancy has done so well hiking that she should try a climbing lesson the next day. He arranges for fellow guide Filippo to take us to the area’s highest mountain pass. “Climbing,” says Diego, “is like dancing” And he does a little shuffle to demonstrate. The next day, Filippo kits us out with hard hats and climbing shoes. It may be mid-summer but it’s freezing up here in the mountains and Filippo kindly lends Nancy his fleece and hat.

We start our climb amid snow and ice and there’s a chill northerly wind blowing. Filippo scrambles up the sheer cliff attaching the guide ropes for us. At this point, Nancy’s face becomes white and pinched. She holes herself up in a little nook at the bottom of the cliff and refuses to move. Considering it a mother’s duty not to let the side down — despite feeling pretty pinched myself — I allow Filippo to put me into a harness and I begin to climb, with another guide shouting instructions below. I’m terrified but my attempt isn’t too embarrassing: I scale half the cliff before bottling out. The second time round, I almost reach the top. Nancy, I’m afraid to say, refuses to budge. Afterwards, Filippo takes us to the Museum of the Great War.