A mother in the US trekked for over 36 hours in freezing cold temperatures, eating twigs and drinking her own urine, after her family's rental car got stuck in mud as they drove to see the Grand Canyon in Arizona.

Karen Klein, 46, walked for almost 50km as her husband Eric - who had recently broken his back - and their 10-year-old son Isaac waited for her to either flag someone down or try to get cellphone service.

The family's car became stuck in mud in a forest after they followed the vehicle's GPS down a dirt track in an effort to bypass roads that were closed or impassable due to the weather.

The family of three from Pennsylvania were on vacation, making their first trip to the Grand Canyon.

"The road was paved and then it became a nicely maintained dirt road and then it became a little more harried," Mrs Klein told CBS News. "And we were thinking, well, this must take us to... the north rim, but unfortunately that did not happen, as the car got stuck in the mud."

It was decided that college professor Karen, a triathlete and marathon runner who is trained in survival techniques, would go look for help, CBS said.

Despite being just 162cm tall, she managed to trudge just over 15km through snow a metre deep when she noticed that the main highway had been closed, said ABC News. She then remembered another entrance to the Grand Canyon National Park just over 20km away, and started walking in that direction.

After running out of her meagre supplies of food and water, she took to eating aspen and evergreen twigs and drinking her own urine - as eating snow can hasten hypothermia.

She also pulled a muscle near her hip and lost a shoe due to compacted snow.

In order to move her leg, she said, she had "physically pick it up and put it forward."

"I could only move it 10 steps at a time," she told NBC News, before getting "very exhausted and sore."

Eventually, it became dark and started snowing, she said.

But she forced herself to stay awake throughout the night, despite growing increasingly exhausted.

"I just kept thinking I have to do this for my son. I have to do this for my husband," she told CBS.

She eventually found a guard's cabin that was closed for the season. She broke a window, crawled in and collapsed, after walking for approximately 36 hours.

Meanwhile, husband Eric had grown increasingly worried.

He and his son slept overnight in the car and the next morning he walked about 25km north to higher ground until he got cell reception, and then he called 911.

"I am in the middle of the forest," Eric Klein said to the 911 operator, according to ABC. "We haven't seen a human being in over 24 hours -- not a car, not a skier, not a hunter, nothing."

Emergency responders on snowmobiles were able to locate Eric Klein's car, and were then able to track Karen Klein at the cabin.

She was hospitalised in Utah and treated for exposure to cold, while Eric and Isaac were treated for frostbite.

"I didn't think I would be out that long," Klein told NBC News, adding that in retrospect, she and her husband should have done a better job of planning the trip.

"We just didn't realise that these roads were closed and these visitor centres were closed," Klein said.

"We didn't investigate that deeply."

Jim Driscoll, chief deputy for Coconino County, said it was "a Christmas miracle" that all three members of the family from Easton, Pennsylvania, were rescued.

'She's in really good shape. Had she not been, she wouldn't have made it,' he said.