In the deadliest incident, at least 45 people died in one village after an avalanche in Nuristan, a northeastern Afghan province on the Pakistan border.
Thirteen people were also killed in an avalanche in northern Pakistan, nine of them in the town of Chitral.
Dozens of houses have been destroyed and people were reported to have frozen to death, trapped in cars.
There were also avalanches to the north of the Afghan capital, Kabul.
"Avalanches have buried two entire villages," a spokesman for the Afghan ministry of natural disaster told news agency AFP of the Barg Matal area in Nuristan.
The neighbouring mountainous province of Badakhshan was also badly hit by snow storms.

Rescuers are experiencing difficulty reaching trapped people, because of bad weather and snow-blocked roads.
The main international airport in Kabul has also been closed because of snow and ice on the runway.
On Kabul-Kandahar highway, police and soldiers rescued some trapped 250 vehicles.
The Salang pass north of Kabul was also closed under as much as 2.5m (7ft) of snow, local police chief Rajab Salangi said, according to Reuters news agency.
At least two stranded drivers have frozen to death. Dozens are marooned there without food.
Officials are warning of more avalanches as snow storms are continuing.