Frying pans are smashing me on the head — about three every second, it seems. At least, giant hailstones are pelting me so hard I could swear they were frying pans — each one slowly flattening me into the side of Mount Kenya. I’m not the only one here swearing, either. Each of the four intrepids in our party is pouring forth a flurry of swallowed expletives almost as hard and fast as the pots-and-pans precipitation. We are all horribly aware that we’re just hours into our three-day ascent Africa’s second-highest mountain.

The Sirimon route we are following will eventually take us to the peak of Point Lenana, 4,985m above sea-level. Even then we won’t quite be at the top of Mount Kenya — that privilege is kept for the Bation summit at 5,199m, which requires all manner of ice-picks, mountain gadgets and several eons more experience than we have between us. Nevertheless we are hell-bent on reaching our goal, no matter how many frozen fingers are sacrificed along the way.

If day one is a shock, night one is simply petrifying. Half-turning to stone in an ice-pit of a campsite, we can’t believe we are just a few miles from the equator. The air is thinner, the temperature lower and conversation more teeth-chattering than ever before. Yet somehow, mysteriously, we find our spirits are rising to the same level as our altitude. The mountain wants us.

The second day brings its reward in the shape of sunlit progress, much like a hike over the moors. We tramp happily along plateaus, and after a while we even forget the dull ache in our calves. Instead, we just stare at the outsized plants in this bizarre foray into fairyland heights. This must the land of the giants at the top of Jack’s beanstalk. Massive cauliflowers and heathers the size of huts are just about all there is to remind us that we are not out on an afternoon stroll wandering England’s green and pleasant land.

Well, that and the elephant dung. As many a guide will tell you with a glint in his eye, wild mountain animals lurk in the thick forests on the lower reaches. Elephants, buffalo and the occasional lion are sometimes seen on low-lying mountain routes. So when we come across a mess of big brown splodge barring our path we are giddy with excitement. Rounding the corner, the route turns out to be mammal-free. We press on. After all, we have a race to win.

We simply want the mountain peak to ourselves, which means getting there first. And to do that you have to start early. Very early. By 3.30am the four of us are still pushing sleep from our eyes as we put one foot in front of the other, lit by the moon. This last heave is hard. It’s icy, more of a climb than than a hike, and you have to use your hands to balance. At 4am, clambering by moonlight, I was in no doubt I was actually climbing a mountain.

Breathing through handkerchiefs to protect us from the cold, unspeaking and unfeeling, we eventually stumble our way to the top. But life, in its sweet way, has played a trick. Punishing us for too competitive a spirit on the mountainside, it let us get to the top terribly quickly. Too quickly. As we collapse triumphant on the frozen peak, nobody else is there. Nor is the dawn.

We can’t very well head straight down again after reaching the top in the dark. So we wait out the night until it finally gives in to daylight — the longest 40 minutes of my life. Even then it is misty. But when the day finally comes, it is ours alone. We have made it to the top of our world, through snow and ice, right by the equator.

Organising a trip: several UK tour operators can organise treks. World Expeditions (020 8870 2600, www.worldexpeditions.co.uk) suggests 10 days, with six days climbing, for £955pp, including transfers to and from Nairobi, guide, park entry and camping fees, porters to carry your bags and cooks who can magic up hot, hearty meals on the mountainside. An equivalent package which includes flights from the UK starts at £1,600pp.

Or try Guerba (01373 826 611, www.guerba.com), Exodus (020 8675 5550, www.exodus.co.uk) or KE Adventure Travel (01768 773 966, www.keadventure.com)

Times recommends

• Britain's top 10 New Year's Day brunches
• Mozambique's lost islands
• The best things to see and do in 2010