The capital's Imam Khomeini International and Mehrabad airports were shut due to poor visibility "until further notice", state television said.
Some 20 provinces in the west and north of Iran were affected by the snowfall that began on Thursday and peaked on Saturday night, with some mountainous areas receiving as much 1.3 metres (more than four feet) of snow according to official news agency IRNA.
Iran's skiiers, who have been denied much action in recent months due to an uncommonly warm winter, were making the most of it.
Iran's drivers were having less fun, with thousands blocked on motorways out of the capital.
Hundreds of Red Crescent teams were mobilised to bring help to the stranded motorists, with a spokesman telling the official IRNA news agency that 6,600 people had been put up in emergency accommodation.
The state gas company said it was bracing for a major surge in demand as temperatures were set to drop to minus-20 Celsius in certain northern regions.
Mayor Mohammad Ali Najafi asked young Tehranis to help municipality workers to shake trees and dislodge the snow in order to avoid further accidents.
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