The Australian Institute of Sport (AIS) scholarship holders were unable to master the snowy conditions, with Chaffer finishing in 10th, and Lincoln-Smith 12th after their two runs down the 1722 metre track.
After top 10 finishes in the previous two World Cup events, it was a frustrating day for the two athletes.
Round six of the eight round Skeleton World Cup was held in St. Moritz on the only natural, non-refrigerated track on the international calendar.
Lincoln-Smith had the unenviable task of being the first slider down the track as heavy snow fell. Chaffer was five places further back, but by the time the event winner, Great Britain's Lizzie Yarnold, took to the track, conditions had improved slightly.
Despite the snowy conditions, the St. Moritz track saw the sliders reach speeds of up to 130km/h.
Both Australians were hoping for improved times on the second run, but with heavy snow continuing to fall, organisers had no option but to cancel the final run.
This gave Yarnold her first World Cup win, on only her second World Cup start, with fellow countrywoman Shelley Rudman second, and Germany's Katharina Heinz in third.
Australian coach, Eric Bernotas, was happy with his sliders' performance, despite the final result.
"I am very pleased with the progression through the week and how the girls raced today, despite the conditions," he said.
"They showed a focus and composure for what was in their control and their performance on the sled showed it. This week's purpose and objectives were to prepare patiently through the week, race intently and confidently, as well as lay a foundation for our return to St Moritz next season for the World Championships.
"I am confident we achieved these objectives and am very happy with the attitude the girls have maintained, ready for each and every opportunity."
After six rounds of the World Cup, Emma Lincoln-Smith remains in seventh place in the overall standings, while Lucy Chaffer has moved one place further up the leader board, to 11th.
The Skeleton World Cup moves from Europe to North America for the final two rounds, with round seven to be held in Whistler, Canada, on February 3.