I had no one to blame but myself - and the triumph of misplaced optimism over common sense, plus a certain familiarity with cold climates due to a Scottish upbringing. Would my friend Penny and I care for a guided tour of Paris in an open-topped car? Yes, we giggled, images of Marianne Faithfull in a sports car overriding any concerns about the wind-chill factor on a cold day in the French capital.
Having been obliged to abandon the warm-wind-in-the-hair idea, we pulled on hats and gloves but, even so, were ill-prepared for what was to come. We found our driver, Vincent - swathed in scarves and dressed like a flat-capped Jean-Paul Belmondo in the Sixties thriller A Bout de Souffle - just behind the Louvre, polishing a headlight on the cream-coloured Citroën 2CV that was to carry us round the city.
The car may be derided as a "garden shed on wheels", but the rolled-down roof of this model revealed deep-pink velvet covers on the back seat, and at least one blanket: in we jumped, and off we set. Vincent pulled and pushed at the car's distinctive gearstick (protruding from the dashboard), swung us round and simultaneously launched into an account of the Louvre, its Pyramid and the masterpieces held within its walls, all in fluent English - when not guiding tourists, he is an international business student.
Within minutes we were heading west along the Right Bank of the Seine, he was pointing out the bouquinistes, and we were pulling the blanket closer against the wind.
The company 4 roues sous 1 parapluie ("four wheels under one umbrella") was set up three years ago by Florent Dargnies, a graduate from a prestigious French business school. Looking for an untapped niche in the crowded Parisian tourist market, he came up with the idea of combining one of France's strongest 20th-century icons with personal tours of the capital.
The Citroën 2CV was designed, like the similarly rounded Volkswagen Beetle, as an inexpensive car for the masses. Unlike modern motoring names, "2CV" actually means something: it is the abbreviation for deux chevaux, two horses, representing the power of the original two-cylinder engine.
The first austere specimen rolled off the post-war production line in 1948. For the following 42 years, it seduced impecunious French consumers with visions of freedom and romance, until its obsolescence became overwhelming; manufacture ended in 1990.
Today's drivers opt for the greater comfort and technological sophistication of more modern vehicles, but the 2CV still evokes nostalgia for a period of post-war prosperity and optimism - not to mention, for many older French people, memories of family holidays along endless routes nationales to the Midi.
The company now boasts a fleet of about a dozen convertible 2CVs, for which Dargnies has scoured the internet and garages across rural France. His firm offers a range of chauffeur-driven visits around Paris, most lasting 90 minutes, as well as longer trips (taking three hours or more) within the Paris region. The idea is now spreading south, with a branch open in Lyon. We were on the "Essential Tour", covering an impressive number of the capital's main tourist attractions in an hour and a half.
We turned on to the Ile de la Cité and drove slowly past the cathedral of Notre-Dame, where our cheerful little car drew curious glances from queuing coach passengers. Vincent then took us around the residential Ile St-Louis, largely overlooked by the crowds, before crossing to the Left Bank. At the epicentre of French intellectualism - and student protests - the commentary switched to Parisian academic and literary life. But as we rattled along the riverside at little more than the pace of an agricultural vehicle, we became concerned about our survival in this small and vulnerable vehicle. The driver of a 4x4 seemed intent on pushing us into the kerb, but Vincent just shrugged, sounded the 2CV's puny horn and let him pull ahead: "Other drivers tend to be kind, they know what our cars are like." On a good day, the 2CV's maximum speed is 90km/h (57mph), with acceleration to match a lethargic mule.
The tour sped by: we craned our necks left for the Musée d'Orsay and National Assembly, before pulling out cameras for a photo opportunity at the Place de la Concorde and the Jardin des Tuileries. Riding up the Champs Elysées was freezing but great fun, while the Arc de Triomphe roundabout confirmed that priorité à droite is at best an optional extra in Paris. We also concluded that perspective is everything: grandiose buildings look even more impressive through the roof of a tiny car.
Vincent talked us along the quieter and more elegant streets of the 16th arrondissement before recrossing the Seine, this time for another photo session in front of the Eiffel Tower. His commentary was wide-ranging, but not particularly profound. While a first-timer to Paris could find it an excellent introduction to the capital's main sights, a regular visitor might regard the narration as merely a recitation of basic information. The secret is to delve deeper: our driver answered with genuine local insight when we asked him specific questions.
By the time we reached the final stop at the steps of Opéra Garnier (having seen the Invalides, the Grand Palais, and the jewellers' shops of Place Vendôme), we were barely the right side of hypothermia and urging Vincent to include a hip flask of cognac as a mandatory part of the back-seat equipment. He laughed and suggested that we go immediately for a piping-hot chocolat chaud.
For a pair of Parisian habituées like Penny and me, the open-topped tour was a fresh way to see the French capital. As always, Paris was beautiful, with the pale sun bouncing off its stone façades and long windows - but next time, we'll go in summer.
Eurostar (08705 186 186; www.eurostar.com) fares from London and Ashford to Paris Gare du Nord begin at £59 return.
Private 2CV tours of Paris are available with 4 roues sous 1 parapluie (00 33 6 67 32 26 68; www.4roues-sous-1parapluie.com). A 90-minute trip costs €50 (£36) per person with a minimum of two people and a maximum of three.
Paris Tourist Office: 00 33 8 92 68 3000; www.parisinfo.comReuse content