Train, tram and bus routes were cancelled, and power cuts were reported across the mainland and on islands.
Schools were to be closed until Tuesday, with classes taking place online, while public service employees were advised to leave work at noon.
Authorities sent out message alerts to mobile phones for citizens to stay home and to use snow chains if they needed to venture out.
Fire-fighters received dozens of calls from people trapped in their cars and others requiring assistance to go to hospitals or to move about.
Cars were seen stranded in thick snow on streets.
Temperatures of minus 10 degrees celsius in the north and zero degrees celsius in Athens were expected, meteorologists said.
Snowstorm "Elpida" is the second cold storm in a week to hit the country.