Each winter, while Britain is in the grip of the big freeze, most of my cycling chums migrate to Mallorca for a seasonal warm-up. It's where you go to jump-start your fitness regime – or, to be more honest, soak up some winter sun in a café you've made an effort to cycle to. That's the trouble with Mallorca. It's for dilettantes. It's too comfy, familiar and well-organised. And despite the challenges of the hills to the north-west, it's mostly too flat.
Real cyclists head for another Spanish island, one that's strangely off the bike radar: Tenerife, in the Canary Islands. As my aircraft came down to land, there was the main reason for my visit – a conical, volcanic summit floating above a sea of clouds like some Bali Ha'i.
Mount Teide is a proper, serious mountain. At 3,718m, it is the highest in Spain (albeit a rather loose definition of Spain), and the world's third-largest volcano. It should, by all accounts, be a siren to cyclists in the same way as iconic climbs such as L'Alpe d'Huez or Mont Ventoux in France are – seducing everyone from lithe Lycra stick insects to emotional, overweight Belgians. Yet, despite its ferocious height, Teide doesn't attract the attention it deserves.
It's the same for the island as a whole. When you're on two wheels in Tenerife, you're something of a trailblazer. This may well have something to do with image. The island is still often perceived – unjustly – as a fly-and-flop destination. Of the 1.6 million British who visit each year, the majority cram themselves into the same small area – Playa de las Americas and neighbouring Los Cristianos – in the south of the island. They don't know what they're missing.
The island is a remarkable farrago of microclimates and ecosystems, at one minute subtropical rainforest, the next a blasted moonscape of volcanic debris. There are relics of lush, steamy laurel woods that covered North Africa and Southern Europe 20 million years ago, cool forests of Canarian pine, coastal deserts and, offshore, colonies of pilot whales and bottlenose dolphins.
Lacing it all together are some of the most serpentine, scenic and breathtaking (in the aerobic sense) roads in Europe. There are many reasons why Tenerife comes out top in a cycling shoot-out with Mallorca. It's much warmer here in winter, flat roads don't really exist beyond the resorts, it's where the professionals train and – because it's not mainstream – you have that frisson of being somewhere that's a touch exotic, exclusive and unconquered. Not many cyclists get to wear the Teide T-shirt. This is not to say that Tenerife is rock-solid hardcore. While beginners are definitely better off in the Netherlands, any reasonably fit cyclist will lap up the challenges on the largest of the Canary Islands.
Other perceptions of Tenerife also need changing. I based myself in the newish Costa Adeje, the aspirational addendum to the big resort of Las Americas. It's unashamedly upmarket, with ultra-modern, faux-Moorish five-star hotels (think The Arabian Nights' Entertainments in bed with the Palm Beach InterContinental), and sleek shopping malls and restaurants that favour Canarian potatoes (papas arrugadas) over chips. The Tinerfeños are upfront about their intentions, describing the Costa Adeje as "how things should be done". These "things" embrace all kinds of zippy outdoor options that don't involve sand and sangria, including whale watching and trekking through the rainforests of the Anaga mountains. But instead I called the very nice Bike Man, who dropped off a hire bike at my hotel for my trip up Mount Teide.
The first few miles were the worst, for two reasons. First, I had to negotiate teeming Las Americas, and second, I'm not a battle-hardened urban cyclist. Having said that, I felt less intimidated than in any white-van-man UK town. The Spanish, like the French, revere cyclists. Road rage is bottled up and kept for fellow motorists (and pedestrians), while saintly cyclists command acres of respect and – more to the point – space. This neutered volatility is all quite surreal, as was trying to find my way through the gleaming Vegas-style gin palaces of Las Americas without a decent map (cartography, unlike cycling, is not part of the local culture).
Things calmed down when I eventually reached the C-822 to Arona, a narrow road to a small town on Teide's south-western flank. I cycle a lot in the French Alps, and found the gradients similar – not hugely steep, but relentless – as the road wound up through an alien landscape that resembled the detritus of a coke oven, yet which was occasionally terraced to create almond groves and vineyards. Within 15 minutes of the coastal pleasure domes, I was in another, ancient Tenerife, a tough environment that yielded only to hard, honest graft.
I had set off in balmy 23C sunshine (by coincidence, Tenerife's average year-round temperature), yet by the time I climbed the 610m to Arona, I wished I had packed warmer gear. I was missing something else: fellow cyclists. On the entire climb along this Rolls-Royce of a road, I came across just one. It was as if Manchester United had thrown open its hallowed grounds to club footballers and only two turned up.
But the cold was getting to me (my fault, for not packing gloves and hat). At Vilaflor – at 1,400m the highest village in Spain – I was ready to throw in the towel. Two reviving cups of coffee (just €1 each, a third of the price in the rip-off Alps) and enough hot water in the washroom to thaw my frozen fingers gave me the lift I needed. I'd come this far and really didn't want to miss the last stretch.
Above Vilaflor, the road surface becomes Formula 1-smooth and Canarian pines kick in. Suddenly, open hillsides disappear into ethereal pinewoods, ghostly in the mist spilling down from Teide's summit.
It was all change again at Boca de Tauce, 2,000m above sea level. Pine gave way to a shattered, other-worldly igneous desert of rusty rock and colossal craters. It was here that I finally gave up: I could have cycled a little further to 2,300m, where the telecabina takes you to Teide's summit, but the cold had beaten me.
Freewheeling back down to Las Americas was like jumping into a warm bath. The beach was busy and people were promenading as I wafted along the traffic-free seafront that curves around the bay all the way back to Costa Adeje. I'd scratched only the surface of the island but could see from my map a maze of roads that would make a stunning Gira de Tenerife.
Airlines including easyJet, Jet2, Monarch, Ryanair, Thomas Cook Airlines and Thomsonfly non-stop from a wide range of UK airports to Tenerife South. The writer travelled with Monarch, which flies from Birmingham, Gatwick, Luton and Manchester.
Costa Adeje specialises in top-end accommodation. The Iberostar Gran Hotel El Mirador, for example, has junior suites for around €345, including breakfast (00 34 922 716 868; www.iberostar.com).
Tenerife Tourism (00800 100 10 100; www.visitenerife.com).
Mountains of winter charm
Work off the Christmas pounds with a session on the pistes. Ebookers is offering a week in Zell am See, Austria, from £391 per person. The price includes seven nights' half board at the three-star Gasthof Limbergof and flights departing Gatwick on 29 January 2011. Lift passes and equipment are not included (020-3320 3320; www.ebookers.com).
Egypt for less
For winter sun on a budget, you can't get much more cheap or cheerful than a week in Sharm el Sheikh for £315 per person. The price includes flights from Luton departing 20 January and all-inclusive accommodation at the three-star Bay View Hotel on the Red Sea coast. The deal is being offered by Lowcostholidays.com (08444 770078; www.lowcostholidays.com).
Experience another new year
Why not extend the festive season and see in a second new year in Hong Kong next year? The Chinese Year of the Rabbit begins on 3 February, with celebrations including a parade, parties and spectacular firework display. Virgin Atlantic is offering flights from Heathrow to Hong Kong from just £567 return. The price is valid for departures between 4 January and 21 March 2011 (0844 209 7777; www.virgin-atlantic.com).