Who is the woman that famously survived a light-plane crash in the arctic in the 1950s?
I'm guessing that this is "Hey, I'm Alive" by Helen Klaben (the female survivor). 

From one of the reviews:


  [...] Flores's Howard five-seater crashed in a heavily wooded region, which no doubt saved their lives. The treetops softened the crash landing yet left the plane listing at an angle, making an uncomfortable shelter for either of them to lie down. Both Klaben and Flores were injured with various broken bones, and each had limited mobility. They were not prepared for an emergency and thus had no winter supplies or extra food. Their scant supply of food ran out after being stretched to siege-of-Leningrad proportions over ten days. I recall a dramatic scene from the movie where Sally Struthers, who played Klaben, discovers a tube of toothpaste which she shows Flores, played by Ed Asner. The two treat the toothpaste as a precious meal, which is exactly how Klaben described it.
  [...]
  Once all food ran out, including the toothpaste, the pair took to re-chewing their gum and by drinking melted snow. I am amazed that they could have survived on only water for five weeks. Flores, hearing a mysterious buzzing in the distance, was determined to find out what it was. I won't spoil the story by revealing if he found out the source of the buzzing or not, but when he returned to the crash site he and Klaben moved camp to a clearing, miles away from the trees. Klaben, who could not walk because her gangrenous toes were decaying, with bone pushing through the skin, was towed along on a toboggan made from the fuselage.


National Post Article on her story

People article

Quote from People:


  When Ralph Flores and Helen Klaben were found alive on March 25, 1963 near the wreckage of his single-engine plane in the Yukon, their names became synonymous with “miracle.” For seven weeks the 42-year-old electrician and the 21-year-old Brooklyn girl had endured pain from crash injuries and temperatures 42° below zero while subsisting on little more than melted snow and a few biscuits.
  
  Flores was flying home to California from Fairbanks and Klaben had accepted his offer of an inexpensive ride to San Francisco. During their ordeal he lost 51 pounds. She dropped 45 and after their rescue had the toes of her right foot amputated because of frostbite. Still, they survived on guts and ingenuity.


They didn't actually "walk-out", they moved the camp to a clearing and were found. Klaben couldn't walk (due to the condition of her toes/feet).