CANNON BALL, North Dakota - Anyone delivering supplies to oil pipeline protesters in North Dakota could face fines, the local sheriff’s office warns. Thousands of demonstrators are hunkered down in the middle of a winter storm, ignoring the governor’s mandatory evacuation order.

Temperatures here plunged below freezing with a wind chill of 13 degrees, but some protesters say they will leave only if the controversial project to carry oil through four states is called off. And the governor’s office said there are no plans for a supply blockade, reports CBS News correspondent Michelle Miller.

Joy Braun said she arrived at the Oceti Sakowin Camp on April 1st. 

“It was snowing then, it’s snowing now,” Braun said. 

“You cook here?” Miller asked.

“I have a little Coleman,” Braun said.

Braun and her cousin, Nathan Bison, showed us where they are hunkering down from the elements, including nearly 40-mile-per-hour winds and below-freezing temperatures, with the help of a wood-burning stove. 
“The governor is saying this is a dangerous way to live in these conditions,” Miller said.

“He sure didn’t care when it was the same temperature as it is outside when he was fire hosing our people,” Braun said. “He didn’t care about it then, so why is he caring about it now?”

“So when he says, Move out,’ when says, ‘Evacuate?’” Miller asked. 

“He has no authority here,” Braun said.

“Are you going anywhere?” Miller asked.

“No, I’m not going anywhere,” Braun said.

Bison said he relocated from Las Vegas to protest the Dakota Access pipeline’s construction. 
“I quit my job to come up here,” Bison said. 
“You did?” Miller asked.

“Yeah, I put my whole family at stake here,” Bison said. 
Despite some violent clashes, Bison is one of thousands who have stood their ground at the site in recent months. Many argue the project is threatening those who rely on the Missouri River for water and is treading on sacred land -- a claim the company building the pipeline disputes.  
Energy transfer partners said their more than 1,100-mile pipeline spanning from North Dakota to Illinois does not cross the Standing Rock Indian Reservation at any point. The pipeline is 92 percent complete. A remaining portion crosses under the Missouri River near the encampment.

CBS News spoke to the company’s CEO Kelcy Warren earlier this month.

“They will not stop our project, that’s naive,” Warren said. “We’re not even crossing any Native American property.” 
Braun argued the land is tribal territory because of a treaty more than a century old. 

“Anybody that says that the 1851 treaty is not valid today – then they don’t believe in the United States Constitution. What are they doing calling themselves an American?” Braun said. 

On Tuesday the White House said the president is being regularly updated on the situation. But the press office said it is not aware of “any impending presidential actions” at this point.