This tent camp sheltering Syrians uprooted by their country’s brutal civil war has lost the race against winter: The ground under white tents is soaked in mud, fights erupt over scarce blankets and volunteer doctors routinely run out of medicine for coughing, runny-nosed children.

The 21-month-old battle to bring down President Bashar Assad has already forced some 3 million Syrians from their homes, according to a new estimate, and cold, wet winter weather is making life increasingly unbearable for the displaced.

Many of the roughly 12,000 people seeking refuge in the tent camp near the Syrian village of Atmeh on the Turkish border fled with just the clothes on their backs, running from intensifying bombing raids by the Syrian air force in recent months.

A 10-year-old boy, Abdullah Ahmed, walked around the camp with a bandaged head and hands after suffering burns during an airstrike on his home.

“I have nothing left except the mercy of God,” said Mariam Ghraibeh, a 60-year-old war widow whose home in the town of Kafr Awaid, about 140 kilometers (90 miles) to the south, was destroyed in an airstrike a month ago. Ghraibeh and her family of 15 now huddle in tents, sleeping on thin mattresses on cold plastic, with two or more people sharing a blanket.

The most basic necessities are missing or in short supply, from toilets to generator-powered electricity. In a tent kitchen, volunteers cook the day’s single warm meal in huge pots on gas burners, and on Tuesday that meant just potatoes.

One tent houses a makeshift school where little learning gets done as dozens of noisy kids, from toddlers to teens, squeeze behind desks to sing, draw and mainly to escape the boredom of the family tent. But most of the children, especially the boys, roam the muddy camp in small groups, some barefoot, others in rubber boots.

The camp is home to some 3,000 children under the age of 12, including about 900 under the age of 1, and they make up the bulk of some 200 to 300 patients a day in the camp clinic, said Dr. Abdel Majid Akkad, a volunteer physician who was born in Syria but lives in Frankfurt, Germany.

Among children, intestinal worms, scabies and head lice are common because of the poor sanitary conditions. The sometimes rainy and windy weather, with temperatures dropping to near-freezing at night, is sending many to the medical tent with coughs and colds. Akkad said there’s a routine shortage of medicines, from antibiotics and drugs against parasites to high blood pressure medication and insulin.

Last week, volunteers pooled their money to buy anti-lice lotions, but ran out before being able to supply everyone. In any case, it seemed a hopeless task, said Akkad, 42, since effective treatment requires washing and ironing the bedding. “How are they supposed to do that?” he said of the refugees.

On Tuesday, Akkad and another doctor on duty stood side by side behind an exam table as mothers brought in their children. Akkad diagnosed a 5-month-old boy with bronchitis, while a nurse gave a shot to a crying toddler suffering from tonsillitis and diarrhea.

“The situation is really bad, winter is already here,” said camp manager Yakzan Shishakly, 34, who owns an air-conditioning business in Houston, Texas, and returned to his native Syria last year to help victims of the civil war.

The number of Syrians driven from their homes by the fighting has risen steadily, and the U.N. refugee agency cited a new estimate by Syria’s Red Crescent of some 2.5 million internally displaced, out of a population of 23 million.

Melissa Fleming, a spokeswoman for the U.N. agency, said it’s difficult to get an accurate count because some areas of Syria are off-limits to aid workers. The U.N. says about 2,000 schools in Syria are being used to house the displaced, while other people have found shelter with relatives. It’s not clear how widespread tent camps like the one near Atmeh are.

In addition to the internally displaced, hundreds of thousands have fled to neighboring countries. They include close to 510,000 people who have registered or are awaiting registration as refugees, mainly in Lebanon, Turkey, Jordan and Iraq, along with tens of thousands who have not registered, the U.N. refugee agency said Tuesday, releasing new figures.

Refugees crossing into Jordan after dark during heavy rains this week were fearful, freezing and without proper winter clothing, the U.N. agency said. It said 60 percent of the new arrivals in Jordan were under the age of 18, including 22 newborns arriving Sunday evening. The agency said it is distributing 50,000 thermal blankets in the largest camp for Syrian refugees in Jordan.

However, there was no sign of major international aid groups in the Atmeh camp, which started out a few months ago with refugees sleeping in olive groves after Turkey slowed the influx of newcomers, said Shishakly, the camp manager.

The camp is run by the Maram Foundation, which was set up by Shishakly and other Syrian-Americans in October to raise funds.

The Turkish Red Crescent has sent tents and distributes breakfast, he said, while he and his supporters buy drinking water and provide a daily warm meal. Another aid group, Medical Relief for Syria, runs the small clinic.

The tents are pitched on a slope that overlooks rolling olive tree-covered hills on one side and a forbidding Turkish military base on the other.

People in the camp say they have been prevented from entering Turkey. While Turkey officially maintains an “open door” policy for Syrian refugees, it has acknowledged delays in accepting newcomers because of strains on its resources and more thorough efforts to vet and register new arrivals.

Some Syrians try to sneak across border, but that requires money.

Mohannad Fahad, a 33-year-old physician from Kafr Awaid, said he is being asked to pay $50 each for his mother, wife and three young sons to be smuggled into Turkey. His family arrived at the camp Monday morning, fleeing air attacks and leaving behind a largely destroyed and deserted town, but he said there is no way he could stay in the camp.

Mohammed Yousef, 45, who fled Kafr Awaid back in September, said most of those trying to sneak in are turned back, and that the only hope is for Turkey to ease restrictions.

In the meantime, Shishakly is trying to make conditions more bearable, by building a storage room, a kitchen and toilets from crude cinderblocks. Some camp residents spread gravel to help keep rainwater away from the tents.

Weather-proofing looks like an impossible challenge, said Shishakly. “We are fighting with time.”

• Karin Laub, Associated Press