NEW YORK -- “Do you know what you’re doing is illegal?”

The warnings from Canadian police are mostly ignored. Towing her baby, video shows one woman struggling through the snow to claim asylum in Canada.

A woman and her baby cross into Canada as police await her CBS News

She’s among the hundreds of U.S. refugees who have illegally entered Canada since President Trump’s first immigration order.

U.S. refugees who cross at an unguarded part of the border are arrested, but once on Canadian soil, they are allowed to claim asylum. At an official border crossing they would be turned away.

In February, 646 U.S. refugees walked into Quebec, a 600 percent jump from February of 2016. Along the whole border, about 2,100 refugees did so in the first two months of 2017, double the number from a year earlier.

Staff Sgt. Brian Byrne CBS News

Staff Sgt. Brian Byrne says he seen the desperation first hand.

“Some people lost their shoes in the snow a couple occasions,” Byrne said. “Somebody crossing barefooted. You know, it’s something. You can tell these people are not used to our climate and all that.”

CBS News was not able to talk to any of the refugees, but immigration lawyers say most are fearful they might be deported from the U.S.

Surveillance cameras allow police to monitor the new arrivals from a command post.

Canadian authorities monitor the border crossings from a command post CBS News

Some arrive by cab, dropped just a few feet from the border. One family that recently crossed is from Colombia. Another was a man from Somalia.

“This is usually the route the migrants will use to cross into Canada,” Byrne said.

Negotiating across a snow bank has become a familiar part of the job for the police.

A Syrian family arrived in nearly zero-degree weather, getting some help before being arrested.

But not all make it. A pregnant Nigerian woman fell just a few feet from Canada.

One woman fell shy of the border, stuck between American and Canadian police, and turned back to the U.S. side CBS News

Caught between Canadian and U.S. officers, she appeared confused and upset. Without proper documents, she was arrested.

A journey more seem willing to risk.