Ammar Kamal, a 35-year-old Syrian shepherd who had sought refuge in Lebanon, along with an unidentified eight-year-old boy, froze to death in snowstorm "Zeina," Lebanon's official news agency reported.
On Tuesday, a ten-year-old Syrian girl died from the cold in a refugee camp in Lebanon's eastern Beqaa region, a medical source said.
Snowstorm Zeina hit a handful of Middle Eastern countries on Tuesday, prompting emergency alerts from local authorities. The storm is expected to climax on Thursday.
Some 1.2 million Syrians have sought refuge in Lebanon since civil war erupted in their country more than three years ago, according to UN figures.
A Palestinian boy in a refugee camp near the West Bank city of Tulkarm died when his family's home caught fire, while another 36 Palestinians were injured in road accidents, according to Palestinian civil defense authorities.
Civil defense authorities added that they had carried out 1,783 rescue operations since the cold snap began on Tuesday.
Four Syrian refugees, meanwhile, died in Lebanon, including a child, who succumbed to freezing temperatures late Tuesday.
The storm, which has been given different names in the countries of the region, has engulfed the region since late Tuesday.
The cold wave has disrupted activity at schools, state institutions and banks throughout the Palestinian territories.