MDOUKHA, Lebanon » The winds spilling down off snow-covered Mount Hermon, bearing the first nip of winter, rattled the broken windows of an abandoned elementary school where Syrian refugees are huddled in this Bekaa Valley hamlet.

Hundreds of thousands of Syrians displaced by the war, many of them stumbling out of Syria during the summer wearing little more than T-shirts and flip-flops, now face the onslaught of winter with inadequate shelter, senior government officials and aid organizations say. "It will be winter outside and winter inside," said Mohamed Khair al-Oraiby, a burly 27-year-old who fled here over the summer with his wife and two infants. "We already wake up early because it is so cold."

With temperatures already plunging to zero overnight in the hills framing this valley, the humanitarian crisis facing millions of displaced Syrians is deepening. More than a million people in need of aid remain out of reach of international relief efforts, the United Nations says.

The inability of international aid groups to cope with the crisis, which has mushroomed in recent months, is partly a question of access to war zones.

More than 400,000 people have fled Syria, and 1.2 million have been driven from their homes within the country, according to the U.N. refugee agency. Some 2.5 million people need humanitarian assistance, and the number keeps climbing. The United Nations said it had reached only one million of them.

But efforts have also been hampered by lack of resources. The United Nations is seeking some $487 million for refugees across the region, of which about 35 percent has been collected.

"The capacity of the international donor community to support the crisis is not happening at the same speed at which the crisis is unfolding," said Panos Moumtzis, the regional coordinator for the Office of the U.N. High Commissioner for Refugees.

Neighboring countries coping with the influx are developing their own plans: Jordan is seeking about $700 million, and Turkey, which has spent $400 million of its own money on state-of-the-art camps with three hot meals daily, is also now seeking aid.

Inside Syria, conditions are even worse. The distribution of aid is plagued by problems of access, security and a lack of organizations to carry out the work, according to aid officials. Most deploy from Damascus, where fighting has been so fierce in recent weeks that aid workers have occasionally been instructed not to leave their houses. Some areas have fallen under the sway of shadowy jihadist forces that eye Western aid organizations as espionage networks.

In November, the International Committee of the Red Cross finally negotiated brief access to the old city of Homs with the fundamentalist militia that controls it. The locals jeered the relief workers for taking more than four months to reach them.

"We’ve been besieged for months," yelled a man wearing camouflage fatigues in a video of the visit posted on YouTube, giving the thumbs-down sign. "Now it occurs to you to come? We don’t want you, we don’t want your food, and we don’t want anything from you."

At least 20 areas within Syria are unreachable because of fighting, aid officials said. Vast swaths of countryside are also inaccessible, including much of the north, because the roads from Damascus are too dangerous.

Families in provincial Idlib are reverting to old methods to survive. In some villages lacking electricity for months, for example, residents have built wood-fired ovens in their backyards, and daylight now sets the rhythm of their lives. They sleep soon after sunset and rise at dawn.

Relief planning is difficult because numbers are elusive and communication is haphazard. In the long-embattled city of Homs, for example, the United Nations listed 223,000 people as receiving monthly food rations, which it used as the number of people in need. But when a fighting lull enabled the Syrian Red Crescent to take a survey, 492,000 people sought assistance.

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 are the United States, at $8.5 million, and Britain, at $7.8 million. The wealthy Arab gulf states have contributed little via the U.N. system, with the exception of Kuwait, which has contributed $1 million.

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, 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, U.N. 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.

The town of about 27,000 people, 12 miles from Syria, has absorbed more than 10,000 refugees. Some are housed 10 and more to a room in 250 drafty cinder-block dwellings with no windows or doors. Clinics are reporting a sudden rise in problems like skin diseases spread by having too many people living together with insufficient hygiene.

A shortage of donated blankets meant distributing just three or four per family, not the goal of one per person. Qatar donated heating stoves, but enough for only about half the refugee families. Fuel is a question mark.

Three schools have absorbed 300 Syrian children, but 2,600 more want in, Fledy said.

In Lebanon, which has banned tent camps, most refugees have been housed in private homes, and are scattered among some 500 towns, said Ninette Kelley, the U.N. refugee representative in Lebanon. The official explanation for the ban was that it wanted to avoid repeating the experience of Palestinian refugees in 1948; twelve camps built for them have become permanent cities, filled with up to 250,000 stateless people.

But the other key reason was that Syria’s allies in the Lebanese government wanted to avoid such visible symbols of the violence that Syria was raining on its own people.

"The government called them guests, as if they were here to enjoy the parks and nightclubs," said Khaled Daher, a Parliament member opposed to Syria.

But with 128,000 Syrian refugees in Lebanon, the government has reached a consensus that it is a humanitarian issue. Officials hope the worst is over, but they are bracing for the day that serious fighting erupts in Damascus, the capital.

On the first day of extensive violence in Damascus last July, 18,000 people crossed into Lebanon in one day.

There are mounting concerns in Syria’s neighboring states about just how many thousands more people they can absorb, and for how long.

"There is a growing concern about security and political stability," Moumtzis said. Syria’s neighbors have so far kept their borders open, he noted, but they are beginning to ask, "Where do we draw the line, because this could affect our own stability?"

© 2012 The New York Times Company