By Lefteris Papadimas
IDOMENI, Greece (Reuters) - Baby Zaynab lay swaddled in a multicolored blanket as her mother gently tried to rock her to sleep.
She didn't get much sleep the previous night, kept awake by the bitter cold which sweeps across the plateau straddling the Greek-Macedonian border and penetrates the flimsy tent which is the only shelter for the 11-day-old baby and her parents.
"I am relying on charity to keep my baby alive," said mother Shukria Al Bakr, 19, trying to suppress sobs as she sat in the tiny red plastic dome among the sea of other temporary dwellings at Idomeni.
"There is no clean water, no food, and I can't breastfeed her," the Syrian said. "All I ask is that they (EU leaders) be merciful to the children here, and let us in."
That is unlikely to happen. European Union leaders and Turkey reached a provisional deal on Friday which would try to stem the influx that has brought hundreds of thousands into Europe in the past year from conflict zones and poverty in the Middle East and beyond.
Among a population of at least 10,000 are an estimated 4,000 children living in squalid conditions at Idomeni, where people queue for hours for a plate of food and fight over firewood to keep warm.
Al Bakr gave birth to her first child Zaynab, or "fragrant flower", in a Greek hospital via caesarian section.
At the hospital someone suggested she give the baby up for adoption rather than return to Idomeni.
"I said no," Al Bakr said, as the baby made a small whimper.
She and Zaynab returned on Wednesday to continue what looks like a hopeless wait for an opening of the border fence.
Under the pact brokered on Friday, Ankara would take back all illegal migrants who cross to Greece, including Syrians, in return for the EU taking in thousands of Syrian refugees directly from Turkey.
Al Bakr, a hairdresser, and husband Hasam, a beauty products salesman, first fled fighting in the Syrian city of Idlib to Aleppo. The war followed them and the couple, who married a year ago, decided to leave their country.
"We want to get to Germany. We have family there," said Al Bakr.
When they returned with baby Zaynab from the local hospital, they found their tent and bedding soaked through.
Other Syrians helped find them another tent and a charity gave them a couple of blankets.
Aid organizations reported a big rise in respiratory infections in the past week because of heavy rain. "There were people living in wet clothes for days," said Vicky Markolefa of medical charity Medicins Sans Frontieres.
Migrant arrivals in Greece showed no sign of letting up, swelling the bottleneck of people trapped there.
More than 46,000 were stuck in the country on Friday, scattered from islands close to Turkey to the waterlogged fields on the northern frontier with Macedonia, halted by the closures of borders along the Balkans route previously used to reach northern Europe.
"It simply defies logic when a Europe of 580 million people hesitates to offer sanctuary to 1-1.5 million persecuted people," Greek Interior Minister Panagiotis Kouroublis said during a visit to Idomeni on Friday.
Greek police distributed leaflets to migrants at Idomeni in Greek and Arabic, urging them to move to official shelters run by Greek authorities.
"The borders are closed. In the camps you will find food and shelter. Do not trust irresponsible people who put you at risk, do not be inconvenienced without reason," they said.
The camp at Idomeni is unofficial and assistance there comes from non-governmental organizations.
After weeks of trekking from Syria to Turkey, then taking the short but treacherous journey to Greece on an inflatable boat, Shukria Al Bakr is starting to wonder if it was worth it.
"It's easier for me to handle bombings in Syria than this situation here. If I had known how bad it would be, I would never have left," she said.
(Additional reporting by Angeliki Koutantou and George Georgiopoulos in Athens; editing by Andrew Roche)