Snow has covered swaths of the Holy Land as storm Alexa continued to cause havoc across the Middle East, bringing misery to hundreds of thousands of Syrian refugees living in tents and makeshift shelters.

In Jerusalem, meteorologists said the worst storm to hit the city for 60 years had left snow up to 50cm deep in some areas.

Ben Gurion airport near Tel Aviv was briefly closed on Friday morning, and major roads were littered with abandoned cars. Motorists were stranded in their vehicles for up to 12 hours as snow blocked highways.

Public transport was cancelled and schools were closed for the second day. Thousands of homes were without power as snow-laden trees collapsed, bringing down power lines.

Nir Barkat, the mayor of Jerusalem, described the snowstorm as a "tsunami", for which the city council was unprepared.

Three evacuation centres were set up to help more than 1,000 people stranded overnight.

Residents of Ramallah, in the West Bank, awoke to blizzard conditions and widespread power cuts. Other areas of the West Bank, including the Palestinian cities of Hebron and Bethlehem, were struggling to cope with heavy snowfalls.

Gaza, whose residents have been forced to deal with 12- to 16-hour power cuts as a result of the severe fuel shortage in the tiny coastal strip, has been affected by heavy flooding as well as the first snowfall in a decade. Dozens of people have been injured.

The Israeli military opened a crossing to allow deliveries of gas for heating and other humanitarian supplies into the blockaded Gaza strip. Four water pumps were due to be delivered to help with widespread flooding.

The snowstorm, which follows a November of record-high temperatures and glorious sunshine, is the second in the Holy Land within a year. Jerusalem and other areas were also blanketed in snow last January.

Storm Alexa has brought blizzards, torrential rain and icy winds to the region this week. Aid agencies have warned that the weather is catastrophic for hundreds of thousands of refugees enduring the bitter cold in flimsy tents and makeshift shelters.

As more snow fell overnight in the Bekaa valley in Lebanon, the United Nations and other agencies scrambled to distribute warm clothing, blankets, bedding, heating equipment and waterproof plastic and tarpaulin.

"More snow overnight here in Bekaa valley. Another brutal night for freezing Syrian refugees in tents," Jeremy Bowen, the BBC's Middle East editor, tweeted.

More refugees are reaching the Bekaa valley each day, crowding into around 250 informal temporary settlements. The Lebanese government has refused to establish refugee camps for fear that those fleeing the Syrian civil war will become permanent residents, as Palestinian refugees did in 1948.

There are already around 1 million Syrian refugees in Lebanon, joining a population of only 4.5 million. Around 2.3 million people have fled Syria since the war began.

Lisa Abou Khaled, a field worker with the UN refugee agency, UNHCR, in the Bekaa valley told the Guardian that the snow was exacerbating already dire conditions for people living in inadequate shelters and tents. Efforts to distribute waterproof materials and blankets were being hampered by the snow, she said.

"These are substandard shelters – and these settlements are expanding on a daily basis. Not only are more refugees arriving from Syria, but some who have been renting accommodation in Lebanon are moving to the settlements as their money runs out," she said.

"Many refugees are leaving their homes with nothing but the clothes they are wearing."

UNHCR said 1,300 refugees had recently arrived in a 24-hour period in a remote area of north-east Jordan called Ruwaished, after walking for days. More than half were children, the agency said.