A blizzard and several avalanches in the Himalayas in central Nepal are reported to have killed at least 26 trekkers and three farmers.
The highest number of deaths - two Israelis, two Poles and eight Nepalese - happened when a blizzard hit a point on the Annapurna Circuit.
Many trekkers returning from the circuit remain out of contact.
BBC South Asia Editor Charles Haviland says it is one the deadliest spells of bad weather ever seen in the region.
Avalanches to the east and west have left 10 more people dead or presumed dead, among them Canadians, Slovaks and an Indian as well as local people.
A French man also died after slipping into the Budhi Gandaki river in heavy rains.
Severe rain and snowstorms in Nepal appear to have been triggered by Cyclone Hudhud in neighbouring India.
Analysis: Phanindra Dahal, BBC Nepali, Kathmandu
It has not been good a year for Nepal's trekking and mountaineering industry. An avalanche on Mount Everest in April killed 16 Sherpas - and resulted in a massive reduction of expeditions to the world's highest peak during the spring season.
The latest disaster comes during the peak trekking period. Thousands of tourists head to Nepal in October, many to enjoy its high altitude mountain passes and pristine beauty. The freak heavy snowfall caught the trekkers off guard.
The tragedy will badly hurt Nepal's tourism, with officials worried about the wider negative message it sends. Trekking and mountaineering are the key backbones of the industry - the major foreign exchange earner for Nepal.
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 4,500m (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.