There was a line in the half-forgotten spoof disaster movie The Big Bus in which the driver hero rebuffs accusations of cannibalism while trying to survive in the back of beyond. "One lousy foot," he rejoins. And whenever Conway is reminded of her nickname she must be tempted to pronounce: "One lousy cheek."
Unfortunately for her it fell to earth in the Olympic Games. Contact was minimal but sufficient both to cost her a place or two and prompt the legend. Conway had all but forgotten it when a television crew arrived in Blackpool to film the fly on the wall documentary Pleasure Beach. They stuck a camera in front of her and, having done their research, asked how "Frosty Bum" was getting on. "I couldn't exactly run away," said the woman herself, now 26, last week. "It's fly-on-the-wall. I can't say I was exactly happy either but it's with me to stay, I guess."
For the past two summers Conway has skated in Blackpool's annual ice spectacular. She will be there again this summer. It is fun, it is making use of her profound talent and now Pleasure Beach is on she might be a star again. Still, it is not the skating she was brought up to do.
Joanne Conway was the last great British ice skating hope. She was adept at the age of 12 and at 14 was British champion for the first time. She was expected to follow in the delicate lines of John Curry and Robin Cousins. It never happened. She skated in two Olympic Games, Calgary when she was 16, and Albertville, finishing 10th and, thanks to the slip, 12th. In 1991 she was fourth in Europe, seventh in the world, maybe only a year and a couple of well-defined triple lutzes away from being No 1.
"I got married and in the end I just drifted out of the sport," she said. "I wasn't well and I wasn't enjoying it." But she spent too many of her formative years attached to ice to leave it behind altogether. She has been enraptured by the deeds performed in Nagano by the American pair, Michelle Kwan and Tara Lipinski. Against the odds and Conway's expectations the Texan sprite Lipinski won and reversed the order in the recent United States championships.
"I was in America at the time and watched them and Kwan was absolutely beautiful. She's an artist, her lines are divine and she looks at home out there. For Lipinski I thought it might be a year too early, like maybe it was for me when I won the British. But technically she's wonderful."
Conway nursed hopes for Nicole Bobeck, the slightly older American whom she knows from the old days. But a disastrous, tumbling short programme dashed all her chances of challenging her teenage compatriots. "She reminds me of me in so many ways on the ice," said Conway. "She's a bit of a wild child but she's fun. My legs used to turn wobbly."
Conway, now divorced, has regrets about her own career's resolute refusal to realise its potential. At 16 she seemed to have it all before her. She was pretty, artistic and they made her Woman of the Year in her native North-east. But her main concern is that Britain has had nobody in her class since. "It's easy to criticise administrative bodies but I wonder if the ice skating authorities give competitors enough support. I never felt they advised me properly."
When Conway first went to Blackpool - "it wasn't planned, I went to the show with some mates and was offered a job there and then" - she could hardly skate for fear. "It was worse than the Olympics. They told me after I was allowed to smile."
At least she is skating again before, as she hopes, embarking on a radio or television career. But something keeps nagging at her. "I wonder whether I should start again," she said. "Just one more time." To show that she is "Frosty Bum" no longer.