On a skiing holiday in the pretty Swiss resort of Grindelwald, Mike Higgins is reminded of the Eiger's notoriety at every turn

'It's enormous!" exclaimed my wife. How right she was. The bulging flanks glistened in the early-morning light, snow clinging to various ridges and overhangs.

It had to be said: the Canadian ski racer's skin-tight orange-and-red race suit really didn't do his rather substantial bottom any favours. But still, he was doubled over trying to recover from a training run for the world famous Lauberhorn downhill race and the last thing the poor chap needed was my wife ogling his buttocks.

And so, by way of distraction, I swept my arm towards the other side of the valley and the Eiger.

The Eiger! Few other words evoke the lethal glamour of mountaineering – and none, surely, lives up to its reputation quite as thrillingly for the dedicated armchair climber. I had read quite a bit over the years about the brave, the foolhardy and the vainglorious who had scrabbled up (and tumbled from) its notorious North Face. But when you drive into Grindelwald – the pretty Bernese Oberland village at its foot – there it actually is: the ogre, bullying the valley beneath, its notorious North Face daring you even to look upon it.

Any decent accommodation vies for the finest view of the North Face, and our hotel, the Belvedere, arguably had among the best. I threw my luggage on the bed and stood on the balcony.

The sun was setting behind the North Face, casting the entire valley in its shadow. Morbid, ghastly visions filled my head: Toni Kurz, dying within yards of the grasps of his rescuers in 1936; Stefano Longhi killed by exposure high up on the face, his body left to hang for two years before it could be reclaimed. Wait a moment: there was a light, shining oh-so-faintly, halfway up the murderous face. Was that some poor soul huddling around his stove, on a knife-thin ledge? Hmm, perhaps not. I recalled reading that there is a lamp above a door leading to the railway tunnel that wends its way to the top of the Jungfrau. Ah, the Jungfraubahn: who but the loco-crazy Swiss would think it natural to run a branch line through three mountains to a terminus 3,454m above sea level? And who but the Swiss would put a well-lit emergency exit door halfway up a treacherous rock face?

Early the next morning, an exceptionally craggy ski guide called Ralph clomped into the hotel lobby and asked if we were ready for our three-day PowderZone experience, an off-piste skiing course organised by our package provider, Powderbyrne. On day one? Perhaps later in the week, Ralph. He glared at my slippers, but to no avail. This being mid-January, our elegant, family-run hotel was half empty, its delightful staff at our beck and call – and I was a mere 20 yards into the lengthy breakfast buffet.

Thankfully my brother was keen, so off the two of them went, leaving my wife, my sister-in-law and me to a slightly less arduous day. First, we dropped the infants off at the hotel's wunder-creche. (One-on-one care, with British nannies! We were living the bourgeois family ski dream.) Then we cruised the rewarding, none-too-challenging red runs of First, the ski area accessed from the top of the village. Across the valley lay the two other main ski areas with equally handsome, if placid, skiing. Kleine Scheidegg and Mannlichen are tucked in beneath the imposing quartet of peaks that dominate the valley: the Wetterhorn, the Eiger, the Jungfrau and the Monch. But be warned, ski bunnies who are used to hopping from station to station will end up chewing their lift passes in frustration. From Grindelwald, both the gondola up to Mannlichen and the train service (included in your ski pass) up to Kleine Scheidegg seem to operate on a glacial schedule.

This, you suspect, is just the way the locals like it. While many owe their living to the Eiger, those who live here appear to embody a discreet but emphatic sense of heimat ("home"). So, the trains are slow, no building is higher than half-a-dozen storeys, and working farms still nestle between Grindelwald and Kleine Scheidegg.

I don't know for sure what my brother and the guide got up to, but the next day Ralph turned up with a smile on his face. The former head of the local ski school, he proved to be a natural, focused teacher. I've lost count of how many ski instructors' tips, shortcuts and mantras I've imbibed and forgotten. But Ralph's I liked: "It's like music: on piste, you ski like Mozart; off-piste, like AC/DC." Or Spinal Tap, I thought, as we veered off the manicured pistes beneath Kleine Scheidegg and floundered about in chopped-up crud.

Before that, just off the Kleine Scheidegg train, Ralph had given us an impromptu lecture on the history of Eiger ascents. Its North Face was first climbed in 1938. "Most summers in the years after that, young climbers would arrive here, pitch their tents in the meadow, and try to climb the face – only the rich could afford to stay in the hotel here," he said, gesturing to the pleasant-looking establishment that still takes guests.

"They watched through telescopes on the terrace and some would return inside to continue their parties when they had seen the climbers fall." Had Ralph yet scaled the North Face? "No, but every time I see it, my fingers itch to climb it..."

Sadly, Ralph would have to make to do with a rather less precipitous peak. The following day, having donned touring skis we were led past the pretty lake Bachalpsee and on up the gentle slopes of Faulhorn. From here we had an impressive, panoramic view of the Lauterbrunnen and Grindelwald valleys.

The descent, through snow glinting in the low afternoon sun, was punctuated by quick lessons from Ralph on how to gauge the angle of a slope with your ski poles, and the digging of a snow pit in order to reveal the weaknesses in the various layers of snow and therefore a slope's disposition to avalanche. (Trust me, it's a lot more engrossing than it might sound.)

We were congratulating ourselves on the wisdom of resort skiing in January – empty slopes, quiet restaurants and hotels, good snow in a low-lying (1,050m) resort and, in the case of Grindelwald, a legendary World Cup race (see box) – when Ralph managed to deliver a true Eiger frisson. Hiking away from the lift system above Kleine Scheidegg, we traversed to the White Hare, a short off-piste itinerary that swoops down from the foot of the North Face. The names of the Eiger Nordwand's features spun in my head: the Hinterstoisser Traverse, the White Spider, Death Bivouac...

Some men and women spent as long as four weeks climbing the most demanding lines on the 1,800m face, others less than three hours (the current record). But all of them had checked their gear and provisions in this gently sloping meadow.

As spindrift avalanches swept the face harmlessly, we set off down White Hare, having encroached upon one of the great stages of mountaineering.

Later that evening I found myself in the rafters of the Grindelwald sports centre dangling from an Eiger-themed rope course. As the instructor who showed me how to use my safety harness warned, it gets tough around the Spider's Web. She was right – at one point I thought I was going to have to ask to be rescued. But no, I conquered my Eiger. And then I, er, popped outside for a doughnut from the bakery opposite.

In the fast lane The Lauberhorn race

Getting there

* Powderbyrne (020-8246 5300; powderbyrne.com) offers seven-night holidays at Hotel Belvedere from £1,415 per person with flights, transfers and half board. The three-day PowderZone experience costs £320 per person. * Grindelwald is accessible from Basel, Zurich and Geneva airports. By train, it can be reached via Interlaken (020-7420 4934; rail.stc.co.uk).

Staying there

* Hotel Belvedere (00 41 33 888 9999; belvedere-grindelwald.ch).

Visiting there

* Indoor Rope Park (00 41 33 854 1290; indoorseilpark.ch/en).

More information

* grindelwald.travel

The locals of Wengen and Grindelwald are proud that the Lauberhorn is one of the oldest ski races – and they don't let you forget it. On downhill day, the Swiss Red Arrows perform a fly-by, which fails to drown out the well-lubricated local supporters, who wear Viking helmets and wave giant flags.

Twenty thousand fans line the 2.65 mile course – the longest on the World Cup circuit and among the toughest – which plummets from the peak which gives it its name, near Kleine Scheidegg, to Wengen.

For this year's race, we took up position beneath the Hundschop, the eye-wateringly steep jump at the top of the course, immediately after which the skiers have to make a wickedly sharp right turn. There are more thrills further down the course: the fastest speed – 98mph – ever recorded in a World Cup event was clocked on the Haneggschuss. It's a thrilling Saturday, and all the more so if, like us, you're lucky enough to see a Swiss racer (Carlo Janka) triumph. Either way, try to find a table at Mary's Cafe near the race finish: the hot chocolate was as good as the service, and the patron reserves a room for the racers themselves.

The 81st Lauberhorn Downhill race ( lauberhorn.ch) takes place on 15 January 2011.