The mountaineers, who were on holiday in Switzerland, had set off to climb the 4,158-meter peak in the Bernese Oberland on Sunday, failing to heed weather warnings.
The overnight temperature dipped to minus 15 degrees, but with wind gusts of 40 to 60 kilometers per hour, would have felt much colder, the Blick newspaper reported, quoting Meteonews.
When they reached the top a snowstorm blew up, and drifting snow prevented the men from beginning their descent.
At around 7pm the men alerted the rescue services in Lauterbrunnen.
However, as it was already dark and the weather conditions were so bad, a rescue team was not able to reach the summit by foot or by helicopter.
“The climbers weren't injured, so we didn't want to put our rescuers at risk,” the head of the rescue service, Urs Schäfer, told the Blick.
An Air Glaciers helicopter was able to land on the peak the following morning and lift the men to safety.
Luckily, the mountaineers sustained no injuries or frostbite despite spending the night exposed on the summit.
They were unable to dig themselves a snow hole because there was not enough snow cover but were equipped with good clothing.
According to Schäfer, the snowstorm had been forecast.
“It is quite common for alpinists to set off without consulting weather forecasts,” Schäfer said, adding that the Estonians had probably learnt their lesson.