More than a million people have crossed through states such as Greece, Macedonia and Serbia on their journey to wealthier European countries.
Fears of a bottleneck of fleeing people stuck between Greece and Macedonia are increasing after Macedonian authorities tried to stem the flow into Europe.
Around 5,000 migrants and refugees are gathered at two locations in northern Greece, with aid groups advising another 4,000 to stay away.
A protest near the Greek village of Idomeni led to dozens of people breaking through metal and barbed-wire fencing along the border.
Afghan men, Salih, Mohammed and Tamim Dost, said they would do anything to reach Europe, including staging a hunger strike.
"Our plan is either to cross the border or to die over here," Salih said.
"There is no place for us to go back to Afghanistan. All the Afghans, especially me, I am a soft target for the Taliban in Afghanistan."
Mohammed said: "This is my plan, that we are staying here. We don't go to camp, we don't want to eat, we don't want to drink, nothing else."
Tamim Dost also said crossing the border was the prerogative, rather than food.
A spokesman for the Macedonian Red Cross at a temporary reception centre on the border, Slobodan Mitrovic, said the wintry conditions make the situation even more desperate.
"By medical aspect, most of them are small kids who have flu and coughing, and, also, depends on the winter conditions, and we have a big change of the temperatures during the night and during the day," he said.
"Most of them are kids, as I say. The other of them are, firstly, women and, after that, the males.
"The last interesting case that we had last night was a newborn baby in the local hospital. So we can say that is the newest and the smallest patient that we actually have."
Macedonia said it is following in the footsteps of other governments, including neighbouring Croatia and Serbia, by only admitting people fleeing from Iraq and Syria.
The move by the Balkan state comes after Austria announced last week it would impose daily limits on the numbers of people seeking asylum or passage to Germany.
Leaders from Italy and Greece have criticised attempts by nations to avoid what they say is those nations' responsibility in the crisis.
In the French city of Calais, British celebrities visited the camp known as The Jungle in an effort to increase awareness of the people's plight.
Actor Jude Law read a letter written by Jewish German author Lion Feuchtwanger, written to Nazis who occupied his home in 1935.
The letter said:
Dear Sirs, How do you like my house? Do you find it pleasant to live in? Did the carpets suffer while the SA men were looting? Red is a strong colour. Hard to clean out. I wonder to what use you put the library. I've been told that books are not very popular in Nazi Germany. In case you should decide to have the bookcases ripped out, be careful not to damage the wall.
Migrants and refugees squatting in the camp have ignored an order to evacuate part of it.
They hope an upcoming court hearing will dismiss the order.
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