BUDAPEST, Hungary —Soaked to the bone and ankle deep in mud, thousands of people seeking refuge in Europe are finding that their path to a new life is growing harder by the hour.

Torrential rains fell as an unprecedented 7,000 trekkers crossed the Greek border into Macedonia on Thursday past rows of camouflage-jacketed police. Children stumbled into mud-filled potholes and had to be pulled back out, bawling, into their mothers’ arms. People struggled to find anything – plastic sheets, garbage bags, even a beach umbrella – to shield themselves from an unrelenting deluge.

But they kept hoping to reach the heart of Europe, where asylum and border security systems are already in danger of being overwhelmed.

“I’m not going to be afraid of anything,” said Waseem Absi, a 30-year-old from Ariha in northern Syria, as he held a disassembled pup tent over his head and trudged up a muddy slope. He said he wants to reunite with relatives in the Netherlands.

The sudden onset of autumn has taken tens of thousands by surprise all along the Balkans route from Greece to Hungary, the main gateway to Western Europe for more than 160,000 asylum-seekers so far this year.

As recently as last week, those making the epic journey, much of it on foot, were baking in a heat wave and free to sleep under the stars. Now they’re without shelter and struggling to keep campfires burning, highlighting the inadequate support provided by European governments at each border crossing.