"I've had a few nightmare experiences in the Alps," she said. "I've stayed in places that had lots of steps and narrow doors, where I've had to drag myself around on wet slushy floors. It's great to be in accommodation like this."
Darke broke her back in a climbing accident in 1993, and was paralysed from the chest down. Having skied for just a couple of days before the accident, she took it up seriously afterwards because it was the best way of getting around in the mountains.
The reason she chose Avoriaz for this, her seventh skiing trip, was that it is one of the three Alpine resorts featured in a new adaptive-skiing programme for skiers with physical disabilities. The holidays are organised by the tour operator Erna Low in conjunction with the retailer Snow+Rock, which provides specialised ski equipment. In most cases, the apparatus used is a sit-ski: a sort of bucket seat mounted on one or two skis, which the skier steers with the help of short poles fitted with skids at the bottom.
Erna Low - which has been selling skiing holidays for 67 years - launched the programme as a result of hiring Jon Lind as a sales executive for the 1997/8 season. Lind, a 29-year-old Londoner, had been a ski rep and instructor for several years when a cousin invited him to join a group of skiers she was taking to Switzerland for the Back-Up Trust, which organises sports activities for people with spinal cord injuries. After teaching able-bodied holiday-makers, Lind found it "exciting to be with people who were so motivated; they weren't holidaying but facing a challenge, and getting satisfaction from their achievements".
The experience led him to set up a company with a friend who had suffered a spinal injury. It organised adrenaline sports trips for people with physical disabilities. But New Trax, as the company was called, was under- financed; and, says Lind, "after two years it became obvious that it couldn't survive". So he went back to working as a ski rep, and then spent several months on the dole before applying for the sales job at Erna Low.
His interest in adaptive skiing (the term avoids the stigma of "disability", and refers to the specially adapted equipment) came up in the interview - and afterwards, when he started work. Erna Low's managing director, Joanna Yellowlees-Bound, says that "Jon is very passionate about the whole thing, and I'm the sort of person who gets enthusiastic very easily". Soon, they were discussing an adaptive skiing programme. "A small company like ours can be very flexible," says Yellowlees-Bound, "so if someone comes up with a good idea that's not too expensive, we can pursue it. Also, the programme could be linked to resorts with which we already worked."
The three resorts in the Erna Low adaptive skiing brochure, Avoriaz, La Plagne and Tignes, all have schools for disabled skiers. This means not only that specialist tuition is available, but also that the lift staff, for example, are familiar with the sit-ski.
That gave the programme a start; still, there were innumerable problems to be solved both in the resorts - wheelchair access to ski-in, ski-out apartments (and, particularly, to their bathrooms, which require widened doorways), insurance, ski-lifts - and on the journey to and from Britain. Lind had to plot a complex route through Geneva airport, which is something of an obstacle course for wheelchair users, and to take into account the fact that not all Eurostar trains stop at platforms adjacent to the station concourse.
Problems such as these are of special importance to the programme because, exceptionally, it is aimed at disabled skiers who want to travel independently. Back-Up and other organisations take groups of disabled people to resorts; but for those who - like Karen Darke - want to go skiing with their friends, Erna Low provides a unique service, at no extra cost.
Indeed the adaptive skiing "brochure" is hardly that: it offers specialist information but all clients - whether disabled or not - book through the company's standard French Alps brochure, at the same price (although each adaptive skier and one helper get a 50 per cent discount on ski-lift passes from the resorts).
For adaptive skiers going to Avoriaz, there is an added incentive: this season Erna Low employed as its resort rep a friend of Lind's, Andrew Moore, an experienced adaptive-ski instructor who is himself a wheelchair user.
"His basic job is to check reservations, receive clients and sort out their problems," says Lind. "But for the new programme it's essential that things go smoothly, and safely.
"So I wanted Andrew to go through a security brief with the adaptive skiers, talking them through the lifts and so on. Some of them may not speak a word of French, and they need to know what to say, for example, when they are disembarking from a lift. That's a basic safety requirement."
(Unfortunately, Moore injured his shoulder and has had to return to Britain for physiotherapy; but he will be back in Avoriaz for the programme's busiest period, when the majority of this season's 26 adaptive-skiing clients will be holidaying in the Alps.)
Organising the programme is highly labour-intensive: Lind is busy with his sales job during the day, and works on the adaptive skiing programme ("it takes a lot of time, a lot of letters") in the evenings and at weekends.
Yellowlees-Bound says of the programme that she has "no hopes for it commercially: I will be pleased if, after the first few years, it doesn't make a loss. But after 15 years selling holidays, it's nice to put something back into skiing."
I spoke to Karen Darke again last week. She is a 29-year-old who works as a geologist in Aberdeen. How, I asked, did she look back on the trip? It was "a real pleasure", she said, "to be so independent".
For details of the adaptive skiing programme, contact Jon Lind on 0171- 584 2841