The United Nations Refugee Agency (UNHCR) says it does not have enough supplies for thousands of refugees in Serbia.
An estimated 10,000 people are in makeshift camps there after European countries limited the movement of people across their borders.
Doctors are warning of medicine shortages and children suffering from hypothermia as the bad weather hits.
Charities and aid agencies have been struggling to cope with a huge build-up of people in makeshift camps after European countries further west limited the movement of people across their borders.
UNHCR spokeswoman Melita Sunjic told the Reuters news agency: "It is like a big river of people, and if you stop the flow, you will have floods somewhere. That's what's happening now".
"There is a lack of food, lack of blankets, we are missing everything," Sunjic said by phone from the Serbian-Croatian border".
Dr Ramiz Momeni, founder of the Humanitas Charity, said migrants in Berkasovo, on Serbia's border with Croatia, urgently need action from international leaders.
He said: "It's an onslaught of people - they just come and come".
"We don't have a chance to treat, we don't have the actual medicine to be given out to them, we don't have any more rain coats".
"As you can see people, children of ten days old, hypothermia, we don't have blankets to give them".
Aid workers said groups of migrants fought on Monday and chanted "open the gate" at Croatian police after a night spent under open skies, lashed by wind and rain.
Daily limit of 2,500
The Balkans have been facing a growing backlog of desperate people after Hungary closed its southern border - diverting migrants, many of them refugees from Syria, to Slovenia.
Slovenia imposed a daily limit of 2,500, while fellow European Union member Croatia - which says it has been letting in 5,000 people per day - has rationed entry from Serbia.
Slovenia has said it can only allow as many people as it can register and send on to Austria, which it claims has put a limit on migrants - a suggestion denied by Vienna.
Slovenian interior minister Vesna Gyorkos Znidar said on Monday: "Yesterday the Croatian side stopped answering our phone calls so we do not know how many migrants to expect, which is making our work very difficult".
Her Croatian counterpart, Ranko Ostojic, said: "Slovenia first said it could receive up to 8,000 migrants (daily), then 5,000, then 2,500 and now it has been reduced to zero. It would mean that the whole burden is being left to Croatia".
Most migrants want to reach Germany, where Chancellor Angela Merkel's spokesman said proposals for a fence along Germany's border with Austria would not stop migrants reaching the country.
The EU has agreed a plan, resisted by Hungary and several other ex-Communist members of the bloc, to share out 120,000 refugees among its members, a small proportion of the 700,000 migrants the International Organization for Migration (IOM) projects will reach Europe's borders from the Middle East, Africa and Asia this year.
