As long as the migrants kept moving, the countries along the route were able to deal with the numbers passing through, refugee officials and aid workers said. And as long as there was a steady flow, the opportunity for tragedy from the impending cold was lessened.

But with fall winds carrying the first hints of frost, and the situation along the borders unresolved, the migrants, aid workers and government officials are anxiously looking ahead. If the numbers increase drastically or, worse, if there are more border closings, there would be an almost immediate backup that would quickly repopulate border camps within a week — some of them open-air, others consisting mostly of unheated tents.

“For now, it is O.K.,” said Uros Jovanovic, the manager of a new processing center being set up in a former psychiatric hospital near the Serbo-Croatian border. “But in 20 days or so, it is going to be very cold here.”

The looming threats have kept migrants on the move, hurrying from border to border to try to reach their destinations — most often Germany and Sweden.