High in the snowy mountains of northern Romania, rescuers heard the trembling voice of a young Ukrainian man -- one in a flood of fugitives now swelled by stricter conscription rules in the war-stricken country.

"I'm so cold," the 21-year-old said. His back hurt after walking for three days over steep mountains with snow-covered peaks in May.

He was just one of thousands who have been fleeing secretly across the border to EU member Romania as Ukraine has tightened its draft rules.

They are "kids who never fought in their lives, scared to go to the battle front", Dan Benga, head of the Maramures Mountain Rescue, told AFP.

"Many of them say that they'd rather come and die on the mountain than die in the war."

Struggling to contain the Russian offensive launched in February 2022, Ukraine has lowered the minimum age of mobilisation from 27 to 25.

It has pushed more Ukrainians than ever to flee to Romania: almost 2,500 in the first four months of 2024, according to Romanian border police, twice as many as in the same period last year.

They risk freezing in the mountains or drowning in the Tisa River that runs along part of the northern border.

- Dead in the snow -

Benga and a fellow rescuer were at 1,600 metres (5,200 feet) altitude when the young man's call reached them.

Benga asked him for precise GPS coordinates and dispatched three rescuers to get him.

He was the 37th Ukrainian saved this year, one of more than 100 rescued in the area since the war started.

But help comes too late for some.

Earlier, Benga's team had been told of two bodies in the snow even higher up the mountain.

They were brought down in body bags, on stretchers.

The men had no identification on them and no baggage could be found.

But Benga believed they were two Ukrainians who had been reported missing almost a month ago.

The sister of one of them had contacted him in desperation.

"It's a tragedy," he said. Many of those who flee are ill-equipped, with "no change of clothes, no provisions".

Since Russia invaded Ukraine, 23 Ukrainians have been found dead on Romanian soil, border police say.

Of them, 13 were pulled from the Tisa river -- a faster route than via the mountains, but dangerous because of the cold water and strong currents.

Benga fears that as the snow melts, more bodies will be found.

- Fugitive 'city of love' -

Those who make it across the border go to immigration centres where they can request temporary protection, granted to Ukrainians fleeing the war.

"The procedure takes approximately five minutes," said the director of one centre, Simona Chioran.

Among the Ukrainians arriving there in vans and cars was a 29-year-old man, travelling with his wife and daughter.

He held his two-year-old in his arms as she slept, head resting on his shoulder, while he answered an immigration officer's questions.

He would not tell AFP how he managed to get out of Ukraine.

Most Ukrainian men aged between 18 and 60 have been barred from leaving their country under martial law.

But some 12,000 have made it to Romania since the beginning of the war, according to border police.

Locals say many soon leave for other countries, but some have settled near the border crossing of Sighetu Marmatiei, or Sighet, 90 kilometres (56 miles) from the immigration centre.

There, in a pizzeria near the wooden bridge over the Tisa river, a Ukrainian man in his late 40s told AFP he left just before the war and now helps some of the Ukrainian men who have fled.

He asked not to be identified.

During the weekends, he says, women who have remained in Ukraine come to Sighet to see their husbands.

They bring them home-made sarmale, a traditional stuffed cabbage roll.

On those days, he says, Sighet becomes like Paris: a "city of love".