Inside a backroom of the Latin Church of Marka in the outskirts of Jordan's capital, Amman, Father Khalil Jaar sifts through a pile of plastic medicine bottles.

It's a mishmash collection of basic medicinal staples for ailments like nausea, coughing spells, and diarrhoea. Yet, this is the makeshift pharmaceutical reserve, which has to protect the health of 1,000 Iraqi refugees during the brutal winter months.

"I asked the doctor here just to give me simple medicines that I could give out to [the refugees] on my own," Jaar told Al Jazeera.

The church leader bought the supplies from a local practitioner using private donations. As the cash-strapped UN refugee agency (UNHCR) warns of withering funds, he says it may be the only aid avenue left for refugees in the country.

Since a lightning offensive by the Islamic State of Iraq and the Levant (ISIL) took over large regions of northern Iraq and Syria in June, thousands of civilians have poured into Jordan, putting further stress upon the desert kingdom's sagging refugee budget.

The season's first severe storm ripped through Jordan in early January. The freezing temperatures affected hundreds of thousands of vulnerable refugees, exposed in meagre shelters. 

Two elderly Iraqis have died from insufficient heating, while several children were taken to hospital with cold-related illnesses. Gas cans and heating stoves were handed out to families, but gas supplies in Marka's poorly-stocked market ran dry during the storm's three-day span.

Jaar says the storm exacerbated the existing funding gap for refugees.

"During the storm we went through 20 cans of gas," Jaar said. "This is a very poor area of Amman, it was impossible to find more fuel."

In Jordan's Zaatari refugee camp some 700 families are still living in tents.

Several hundred men, women and children rushed to emergency shelters set up by the UN refugee agency, UNHCR, to wait out the worst of the storm. Its aftermath brought new challenges to the sprawling camp of approximately 80,000 displaced Syrians, one of the largest worldwide.

"Well above 70 tents completely collapsed," Nasreddine Touaibia, a UNHCR public information and mass communication officer, told Al Jazeera. "What these families have lost in the storm is the tent - and everything inside it."

Over 100 new caravan shelters were donated this week, with more shipments likely to arrive by the end of the month. As winter continues, Touaibia says the UNHCR is hoping to phase refugees out of tents.

The UN representative confirmed delivery of more than 200,000 blankets to the refugees in the past four months, plus cash assistance to 27,000 of the most vulnerable families.

Gulf nations have pledged to bolster their financial support for 2015.

During a visit to Jordan on January 14, UN High Commissioner for Refugees Antonio Guterres said the UNHCR would need over $3bn to support an ever-expanding emergency for some 3.2 million Syrian refugees in neighbouring countries this year.

At least 620,000 Syrians are registered with the UNHCR in Jordan, although the government estimates the number is as high as 1.4 million. About 44,000 Iraqi refugees have also registered.

Back in Marka, Jaar sees his own funds for the Iraqi Christians his church supports dwindle. He's worried the people here will simply be forgotten.

"No one is asking about them; not the government, the UNHCR, nor the community leaders," Jaar said. "And now I am starting to fear that no one will come."

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