Groups included women and children where journeys from Italy lasting 36 hours have been made harder by what forecasters describe as the kind of snowfall seen only “once every 30 years”.
Up to a dozen have reached France by crossing the mountain range each day but rescuers expect to find bodies of African migrants when snows melt in the spring.
Attempts by road have been foiled.
Authorities in northern Italy last month said the situation hit “emergency levels” and called for more security measures near the border.
In the Italian mountain town of Bardonecchia, three men were seen pausing after battling the treacherous terrain in temperatures as low as -9C (15F).
The group, attempting to cross into France, also included a 24- year-old Senegalese man, a 31-year-old from the Democratic Republic of Congo and a 37-year-old from Pakistan.
They managed to cross the border but were too weak to continue and were returned to Italy.
One rescuer spoke about finding the migrants.
“They were visibly cold and poorly equipped, but they didn’t want to turn back so close to their final destination,” he said.
Another helper added: “We told them every way we could that they were risking their lives by continuing – they were in gym shoes and tracksuits and were completely soaked.”
Migrants began heading across the mountains last spring as the French authorities tightened up on attempts to cross in the coastal Ventimiglia area.
Last year, 171,635 migrants arrived in Europe by boat from the Middle East and Africa, down from 363,504 in 2016 and a million in 2015.
The International Organisation for Migration estimates 20,000 have died in the Mediterranean while trying to reach Italy in the past two years.