The agency says Syria's neighbours are already struggling to cope with the influx -- an estimated 600-thousand people.
And, as Kerri Worthington reports, the non-government aid agencies working with the refugees agree.
Winter has hit the Middle East with a vengeance this year, and Syrians who've fled the violence in their country are among the hardest hit.
Snow has blanketed refugee camps in Turkey and Lebanon, and even Jordan has experienced rare snowfalls.
The UNHCR says there's already been a three per cent increase in refugee numbers in Turkey since the year-end figures of 2012.
The head the World Food Program says more aid must reach Syrian refugees to meet expanding needs caused by the cold snap and the increasing numbers of people seeking help.
Ertharin Cousin was speaking ahead of a tour south-eastern Turkey, where 12,000 refugees have set up home along the border with Syria.
She says the aid effort costs about 25 million dollars a month, but more is needed.
Her calls are backed by international aid agency World Vision.
Spokeswoman for World Vision in Australia, Anthea Spinks, says Lebanon is struggling to cope with the almost 140-thousand registered refugees fleeing violent fighting in Syria.
Ms Spinks says those without permanent shelter will be hit hardest by the cold weather.
"We're experiencing sub-zero temperatures, and it's not something that we think about for the Middle East, although they do have quite cold winters normally. But this is a particularly cold winter. The estimates are that it's the worst in at least a decade. Now for populations that don't have appropriate housing, that don't even have sufficient blankets if they're living outdoors, obviously that's a big concern."
World Vision workers have called for the world's attention to return to the Syrian situation, nearly two years after the uprising against the Bashar al-Assad-led government began.
Anthea Spinks says when focus moves to other issues it's harder to raise resources they need." It makes it a lot harder for us to keep the momentum and keep the attention on this crisis.
Obviously a lot of the attention is also not just on other events, but also on the events inside Syria itself. And we're finding that we're particularly needing to maintain the attention and the focus on the people that have been fleeing the crisis.
We're working particularly with communities in Lebanon and we've seen that over 140,000 people are officially registered with the programs in Lebanon, (although) we think there are many more thousands.
There are over 500,000 people in the region that have fled Syria in the last little while, so there's a huge number of people that are moving, and we're very concerned that we can actually provide the assistance that they need, both the material assistance, but also the psychosocial assistance."
Inside Syria, humanitarian organisation Medecins Sans Frontieres says its clinics are struggling to cope with the number of civilians seeking medical care.
An MSF team has recently visited the Idlib province in the country's north-west, with reports that patients are travelling long distances across dangerous territory to be treated.
Emergency operations manager, Dr Mego Terzian, says the clinic is running without electricity or water, and under constant threat from shelling.
"We are seeing mainly polytrauma cases due to shellings. There is also some wounded cases with gunshot coming to our clinic. We are also performing other emergencies not related to violence because there is no access to the healthcare, so we are obliged to take care of any case coming to us."
Dr Terzian says MSF suspects government-controlled areas are suffering, too.
"Honestly, don't have any idea about what is going on. But if some doctors from the government zones are referring patients to us, I guess they have serious problems as well. They have apparently shortages of some important medicines to do anaesthesia. They have shortages of consumables and reactives to perform blood transfusion, so they have problems as well."
The Syrian refugee situation is to be discussed at an international conference of donors for Syria in Kuwait later this month. (30th January)
And Syria continues to top the agenda at the UN, with the five permanent members of the UN Security Council set to discuss the deteriorating situation at the end of January.
Russia and China have been traditional Syria allies, while the United States, Britain and France have been calling for President Bashar al-Assad to step down and actively support the opposition.
There's been no indication any side is about to change its stance.
And Syrian Deputy Foreign Minister Faisal Mekdad has told the BBC President al-Assad is sticking around, hoping to contest elections next year.
"The President and many other candidates will go to the people, put their programs and be elected by the people. So the ballot box will be the place where the future of the leadership of Syria will be decided. What are they doing in the West? It is a coup d'etat if we listen to what the armed groups and those enemies of Syria are proposing."