"We have some who have crossed by bike in the dead of winter," customs' inspector Goran Stenseth told AFP on Monday. "The cold, the snow, the darkness... All of this presents a real challenge to these people."
Some of them may have also spent some time in Russia.
"About 150 people have crossed the border so far this year, mostly Syrians," he said. "The numbers have really taken off this year."
Kirkenes is about 4,000 kilometres (2,500 miles) from Damascus as the crow flies. Temperatures in winter can regularly drop to minus 15 degrees Celsius (plus five Fahrenheit).
In 2014, only a dozen asylum seekers entered Norway at the Storskog border crossing, guarding what during the Cold War used to be one of the only borders dividing the USSR and NATO.
It is difficult to find out why the Syrians arriving in Kirkenes chose that route. Norway, which is not a member of the European Union but belongs to the Schengen Area allowing free movement of people, has a right-wing coalition government that includes the populist anti-immigrant Progressive Party.
The oil-rich nation has a relatively restrictive refugee policy, especially when compared to neighbouring Sweden. Sweden recorded the second biggest number of asylum applications in the EU in 2014 after Germany -- 13 percent of all applicants, although as a proportion in relation to its population size, the country is shouldering the biggest burden in the bloc.
Because the border is closed to pedestrians, some have cleverly found a loophole by biking into Norway. The Kirkenes police have seized around 20 bikes, and issued fines up to 6,000 Norwegian kroner (around 650 euros or $800) to Russians and Norwegians who have made a business out of driving migrants over the border for a fee.
"We don't want these vulnerable people to be exploited," Stenseth said. "We are trying to figure out if they're being transported as part of an organised trafficking ring but so far there is nothing to indicate that," he said, noting that the Syrians were crossing alone, as families or in small groups.
"Those who arrive here appear to be in good health and happy to arrive in Norway," he said.
Contrary to what may happen in other European countries, the migrants are not turned back at the border. Once they've crossed into Norway, they are immediately transported to Oslo where they are registered for processing.
According to Norwegian immigration authorities, just under 1,000 Syrians have sought asylum in the Scandinavian country since the beginning of the year.
In 2015 more than 300,000 refugees fleeing poverty and conflict in their homeland have crossed the Mediterranean in an attempt to reach Europe. More than 2,500 died during their crossing, according to an official count published on Friday by the UN refugee agency.