A group of Syrians, including children, had tried to enter neighbouring Lebanon late on Thursday through a smuggling route but were caught in a fierce storm.
The Lebanese army and civil defence said on Friday they had retrieved the bodies of 10 Syrians, including two children and six women.
But the toll has since increased.
Lisa Abou Khaled, a spokeswoman for the UN's refugee agency, said at least 13 Syrians were confirmed to have died in the incident.
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"The victims were trying to cross an arduous and rugged passage in freezing temperatures," the UNHCR said in a statement.
"Others in the group, including a pregnant woman, were discovered in time and assisted by nearby residents and the Lebanese Armed Forces and Civil Defence to reach hospitals before they froze to death."
A Lebanese army source told AFP on Saturday that the toll had reached 14.
"The army retrieved a total of 12 bodies on Friday, and one person died at the hospital. Another body was found on Saturday, bringing the total to 14," the source said.
Lebanon, a country of four million, hosts just under a million Syrians who have sought refuge from the war raging in their neighbouring homeland since 2011.
Many live in informal tented settlements in the country's east and struggle to stay warm in the winter.
The UN's children's agency UNICEF said on Saturday it was distributing blankets, warm clothes and heating fuel.
"More children could be among the dead as residents in the area and the Lebanese authorities continue to look for people who are reportedly trapped in the mountainous in freezing temperatures and snow," a UNICEF statement said.
"The brutal wars have to stop and we all need to step up our generosity and assistance for the most affected children. We have no excuse. We cannot continue failing children!"
In 2015, Lebanese authorities introduced new restrictions to curb the number of Syrians entering the country.
Lebanon and Syria share a rocky 330-kilometre (205 mile) border with no official demarcation at several points.
