Sitting in fourth place after the first run at the Sanki Sliding Center, the duo could not slide onto the podium with their final run, posting a combined time of one minute, 39.840 seconds, just 0.05 seconds back of bronze medallists Juris and Andris Sics of Latvia.
German pair Tobias Arlt and Tobias Wendl took gold in a combined time of 1:38.933 while Austrian brothers Wolfgang and Andreas Linger took silver in 1:39.455.
Calgary's Snith, and Walker, of Cochrane, Alta., were seventh overall in World Cup action this season, and earned their first-ever World Cup podium finish with a bronze in Koenigsee, Germany in January.
Their result ties the best finish for Canada in a luge event, set by Calgary's Alex Gough, who finished fourth in the women's event on Tuesday.
Snith and Walker were the first tandem down the track during the first run, and set a track record, completing the course in 49.857 seconds.
The record wouldn't stand long, as the gold and silver medallist teams took turns breaking the mark.