Of the six winter sports funded to the tune of 14 million pounds by the government agency, Britain's best chance of podium finishes is in skeleton where World Cup leader Lizzy Yarnold and world champion Shelley Rudman are amongst the favourites.
There are also high hopes of success in the new Olympic event of slopestyle in which freestyle skier James Woods is the reigning overall World Cup champion.
In Vancouver four years ago Britain managed just one medal when Amy Williams won skeleton gold.
"If achieved, (three medals) would demonstrate the fantastic momentum created by London 2012, where additional investment and focus on developing our high performance system has benefitted summer and winter sports alike," UK Sport chief Liz Nicholl told a news conference.
"This is the best supported of any previous Winter Olympic teams and the best prepared."
Nicholl said the upper range of British medals was seven "if everything went right".
As well as in skeleton and slopestyle, Britain has realistic medal hopes in speedskating with Elise Christie a bronze medallist in last year's worlds while the women's curlers led by Eve Muirhead are expected to be challenging for the podium.
Britain's team for the Winter Olympics is expected to number 50 with the final names being confirmed next week.
The last time Britain won three medals in a Winter Games was in Garmisch in 1936
(Reporting by Martyn Herman, editing by Justin Palmer)
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