The Syrian government has allowed only eight foreign aid organizations to operate; all were already working in Syria before the uprising started in March 2011, helping Iraqi refugees. Seven employees of the Syrian Red Crescent have been killed.

The largest aid donors through the office of the United Nations High Commissioner for Refugeees are the United States, at $8.5 million, and Britain, at $7.8 million. The wealthy Arab gulf states have contributed little via the United Nations system, with the exception of Kuwait, which has contributed $1 million. But much more money comes through other channels. In total the United States has spent is a little less than $200 million, according to USAID, while Britain has committed more than $85 million, according to the Foreign Office.

Now the cold is adding another layer of need. Middle Eastern winters can be bitter, with snow in some areas and chilly winds slamming across the deserts.

Since only about 35 percent of the $70 million budgeted for winterization has been funded, only the most vulnerable third of the population will get help, Mr. Moumtzis said. Or as one senior diplomat put it, the refugees will be fed, “but not generously,” and they will be clothed, but “they will be cold.”

Efforts at triage are readily evident. In the Bekaa Valley, 10 to 15 families arrive daily, United Nations officials said, and 75 percent are women and children.

“Can we get those other 150 houses moving? Because the terrible winter temperatures are here!” pleaded Ahmed Fledy, the deputy mayor of the northern Bekaa Valley town of Ersal, to an aid worker entering his office.