As the phenomenon of asylum seekers looking to enter Canada illegally spreads beyond Manitoba's border, aid agencies say they are feeling the pinch to provide care to the influx of people.

At least six asylum seekers were arrested as they crossed into Surrey, B.C. this weekend, in addition to eight who crossed into Emerson, Man.

The Salvation Army centre in Winnipeg says the spike in asylum seekers is leading to a shortage of free space.

"The numbers are growing fast and we're challenged by that," said Major Rob Kerr. "We do have opportunities to move things around and make more space, but it's getting tight."

Meanwhile, the eight arrested in Manitoba spent seven hours in cold temperatures, hiking through deep snow.

"As soon as we walked through the snow, I thought we were dead," said Abdulrahman Mohamed, one of those arrested. "I couldn't feel my feet by the end of it."

Mohamed -- who is from Somalia, one of the countries Trump is looking to ban travellers from -- had applied for refugee status in the U.S., but feared being deported.

Asylum seekers say U.S. President Donald Trump's proposal to ban travellers from seven Muslim-majority countries entering the United States has left them feeling desperate.

But despite the rash of border crossings now being seen across the country, the immigration minister isn't convinced that it's a trend.

"We need to see what happens over the next little while," said Immigration Minister Ahmed Hussen. "We can't really determine that this is a trend moving forward."

If asylum seekers reach Canadian territory, they are entitled to go through a claims process after being arrested because Canada is a signatory of the UN Refugee Convention.

Should their claim be rejected, they could be returned to their country of citizenship.

"We have international obligations to make sure that if you're in Canada, and you're on Canadian soil, and you claim asylum, we have to give you access to a fair hearing," he said.

Manitoba officials say they're concerned that there could be a great number of asylum seekers looking to cross the border once the weather warms up in the spring.

Canada's Public Safety Minister is planning on meeting with his U.S. counterpoint in the coming weeks to discuss the issue.