Until the recent cold snap, it had been a mild winter – remember the daffodils in December? For some this was no doubt a good thing; for me, it didn't feel right. Like many British people, I need a protracted season of cold, miserable winter weather in order to see me through the protracted, miserable summer.

Then the solution appeared to me. A headline in the local paper about a man who had fallen 60m down Ben Nevis, and survived. Now there was an individual determined to do something about "failed winter syndrome". You head north.

The Ice Factor in Kinlochleven, 20 miles south of Fort William, was offering what I needed. A two-day winter mountaineering experience, with the first day on its indoor ice wall, the second on the hills.

As I drove up from Glasgow, the Loch Lomond hills looked voluptuously inviting – white-capped and basking in sunshine – but when I reached the Ice Factor the forecast was more promising: snow falling on higher ground, turning to sleet with considerable avalanche probability. The next day, scheduled to be my day on the hills, was summarised in a single phrase, "No sunshine." I could not have asked for more.

Built inside the grand Edwardian shell of an aluminium smelter, the Ice Factor is one of those marvellous monuments to one man's eccentric determination. Jamie Smith was a keen winter climber who had seen friends lose their lives in the mercurial and sometimes vicious Scottish conditions.

His dream was to build an indoor ice wall on which climbers might train before committing themselves to the capricious outdoors. Then, while at college, a chance meeting with a refrigeration expert confirmed that an ice wall was feasible. A prototype was built, followed by the real thing: a 13m‑high indoor iceberg, the largest in the world, housed in a room that is kept at about -2C.

I started with a session on the indoor rock wall. "To loosen up," as Jamie Bankhead, my climbing guide and the centre manager, put it. As I'd not been rock-climbing for a couple of years it soon had the opposite effect: I could feel my forearms tightening as I tried ever harder to make up for the lack of balance and power coming from my legs.

Two hours later, fully loosened up, Jamie gave me a straightforward explanation of how to climb a vertical ice wall using two ice axes and boots with spikes on the toes. "Keep your heels down. Press your groin in. Keep the axes up and close together."

You would think it might be easy. Just whack an axe in, shift up, kick a toe in, shift up, and so on. But my first attempt did not go so smoothly. I whacked in an axe, then the other, kicked toes in, held it there – wow, already feeling the strain – heels lifted by a few millimetres, toes slipped out, then I hung like a failed gibbon from the axes with toes scrabbling at the ice. It was like a scene from Touching the Void in every way, except that I was only two centimetres off the ground.

Ice climbing is all about balance and poise. Concentrating very hard indeed, and with much advice from Jamie below, I made it halfway up the 13m wall. There had been one precious moment when suddenly the combination of axes, crampons and body balance clicked into place. I rose without effort.

I felt like a human fly, Spiderman, invincible. Two moves later I'd lost it completely. Sweat was rolling off me. I'd used far too much shoulder power to make it this far and now I was paying the price.

The two-hour session passed in a blur of exhilaration and fatigue. I went to bed that night exhausted and slept like a baby.

The next morning Glencoe was as bleak and beautiful as I'd ever seen it. The geology here means that the ridges on either side of the great sweeping valley have very few access points. "In summer the Aonach Eagach ridge is the classic," said Jamie. "But once you're committed, you have to finish it – there's no easy way off it."

We were going to tackle Stob Coire nan Lochan, a well-known 1,115m peak, perhaps too well-known judging by the number of cars parked by the A82 in Glencoe. Avalanche risks, however, meant everyone was being forced to head for the same goal.

After a long walk in we donned crampons and headed through knee-deep snow past the small loch, and up a steep slope towards one of several buttresses. We passed the time discussing when, and if, it was ever correct for the guide to abandon his customers and save his own skin. Jamie knew all the relevant cases, but didn't think it was going to be an issue for us. I wasn't so certain.

The last kilometre, up a 45-degree slope, took me down to a T-shirt despite the flurries of snow – and icy rain. The temperature was rising. Finally we were standing under the buttress. When Jamie set off there were already two other parties struggling up the slope towards us, clearly bent on the same route. I paid out the rope as Jamie climbed, dodging the snow that came tumbling down. The clouds were closing in. When Jamie's shout – "Climb When Ready!" – came, the other two groups were waiting for me to leave.

I set out, determined not to be hurried. However, it proved to be an easy scramble up the 50m to where Jamie stood. We repeated the manoeuvre. Now the third pitch. "This is the one where you don't take pictures," said Jamie. "I want your hands on that rope all the time."

Looking up I could see why. The buttress had narrowed to a series of sharp needle rocks, rising into the mist. On either side were substantial drops on to steep snow gullies. Jamie went slowly, setting the rope through slings and chocks for me to remove on the way up – protection, as mountaineers call it. The other two groups came up and chose to traverse into the left-hand gully, missing this final challenge. "You can always take that traverse," Jamie shouted down. "Not a problem."

I was cold and tired, but aware that the next 20 minutes were what I had come for. I was not going to give up now. I started up. There was a sling to remove, basically a large looped band that was thrown over one of the needle rocks. Then a chock. As each of these came out, there was a few metres of rope to the next protection, and I was aware that a slip would be painful and embarrassing, though certainly not fatal. The cloud, caught in an updraught, suddenly rose and I glanced behind to catch a brief glimpse of the mountains and valleys spread out below, a dizzying sense of space and height, and me clinging to this rock no wider than my shoulders.

There was a column of sheer rock that my face was pressed against. No footholds or handholds. How on earth was I supposed to climb it? I fished around above my head with an axe, searching for a hold, but there was none. I tried scrabbling at the sides of this insurmountable obstacle with my crampons. They found no grip.

Finally I put both axes over the top of the rock and locked them together. I was pretty sure this was not in any climbing manual. My arms were fully stretched. Then I shimmied up, using sheer brute force and some knee clenches on the rock. Shaking with relief, I reached the peak where the narrow ridge flattened out. All I had to do was walk 10 paces along an icy path, as broad as my boots, to safety.

"Don't fall now," shouted Jamie, "there's no protection on this bit."

Glad to have this reminder, I scampered across. Now there was just a short scramble to what should have been a magnificent view. Instead there was an icy roar of wind over the ridge, a scouring of sleet and a 360-degree panorama of cloud. "I could tell you what you're missing," said Jamie, "but you'd only weep."

My perspective on ice climbing at that moment was as harsh as the climate: it's very hard work, it involves periods of being cold and wet, and it doesn't necessarily involve any views or even a glimpse of sunshine. Four hours later, in the bar of Kinlochleven's MacDonald Hotel, my toes warmed up, I added to the list: superb workout, totally exhilarating, and wild – exactly what I had come for. My Scottish winter is complete. I'm fully innoculated for an English summer.

• The Ice Factor (01855 831100, ice-factor.co.uk) runs ice-climbing and mountaineering courses all year round. An indoor day combining rock and ice is £65pp. A day on the hills costs £180 for the guide with a group of up to six. The Ice Factor also runs Xscape snow slope in Glasgow (xscape.co.uk/braehead) and plans to build an ice wall there too. The MacDonald Hotel in Kinlochleven (01855 831539, macdonaldhotel.co.uk) has doubles from £64 B&B, cabins from £10pp, and camping for £6pp. For further information on snow sports in Scotland, see visitscotland.com/surprise