The highest number of deaths – two Israelis, two Poles and eight Nepalese – happened when a blizzard hit a point on the Annapurna Circuit.
Scores of trekkers remain out of contact while returning from an Annapurna Circuit pass.
Meanwhile five more climbers are presumed dead after an avalanche in nearby Manang district.
Officials say four were from Canada and one from India.
Three Nepalese farmers have also been killed in a separate avalanche in the same area.
Severe rain and snowstorms in Nepal appear to have been triggered by Cyclone Hudhud in neighboring India.
Cyclone Hudhud hit south-east India earlier this week – satellite pictures now show it moving away from Nepal towards China.
The bad weather hit a resting place 14,800ft above sea level, not far below the Circuit’s highest point, the Thorung La pass.
The trekkers who were killed or remain missing were on their way down.
An army official co-ordinating the search operation said two military helicopters had been sent from the capital Kathmandu to assist the rescue operation.
Thousands of trekkers visit the Annapurna Circuit every October, when weather conditions are usually favourable for hiking trips.
What appears to be a freak snowstorm a little under the highest pass caused mayhem, with many people still believed to be trapped in snow.
Only a little to the east, near Mount Manaslu, a French man died after being swept into a river.
The deaths come just months after 16 Sherpa mountain guides died in Nepal’s worst ever accident on Mount Everest.
Nepal’s high peaks attract some of the world’s best climbers – but trekking is generally safe and appeals to masses of ordinary outdoor enthusiasts.
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