British Olympic chief Simon Clegg says one medal at February's Turin Games would represent a success for Team GB.
Clegg believes the team can compete for medals
Britain won a gold and a bronze in Salt Lake City four years ago but expectations are low this time around.
"If we can deliver a medal of any colour that'll be an excellent result," BOA boss Clegg told BBC Sport.
Rhona Martin led the women's curling team to a shock victory in 2002, with women's skeleton star Alex Coomber also claiming a bronze at the same Games.
Britain has won an average of one medal per Games since the Winter Olympics began in Chamonix in 1924.
Four years ago, they would have enjoyed their most successful Games since 1936 if Alain Baxter's slalom bronze had stood.
The Scot was stripped of his medal after failing a post-race dope test.
Britain has never won an Olympic skiing medal - Georgina Hathon finished fourth in the women's slalom in 1968.
And while British skiing and snowboarding boss Mark Tilston is hopeful of breaking that duck in Turin - possibly with skier Finlay Mickel or snowboarder Zoe Gillings - he has set a more modest target.
"To continue to get the level of funding we receive we're hoping for two top eights and another four top 15s," he said.
Britain's elite winter Olympians received about £2.5m in lottery funding in the four-year cycle leading up to Turin, shared between alpine skiing, snowboarding, curling, bobsleigh, skeleton and speed skating.
But detractors will argue that this represents an expensive outlay for a single medal.
"The problem is you can't predict where that medal will come from," said Clegg. "You have to make that investment."
Bromley is up to fourth in the world in skeleton bob
In Turin, Scotland's Martin will defend her curling title with a new team, though they are ranked only sixth, while Coomber has retired and Baxter's form has tailed off.
But there are signs of a new guard ready to take on the task of dragging British winter sports from its torpor.
Skeleton star Kristan Bromley won the 2004 World Cup and European Championship, Gillings has reached fifth in the world in snowboardcross, and downhill skier Mickel achieved a career-best 10th in a World Cup race in Wengen.
Jackie Davies and Nicola Minichiello also became the first British women to win a bobsleigh medal at the world championship when they clinched silver.
"The challenge for us is that we're never going to be able to deliver that level of results on a consistent basis because of our lack of facilities," said Clegg.