Aron Ralston has to be on the top of any badass outdoor adventurer list. When I read the Outdoor Magazine with Aron on the cover, I could hardly believe his story (now told through the film 127 Hours). The article went into extreme detail of Aron's hiking trip in Canyonlands Park in 2003, which turned into a grueling ordeal.
Without adequate food or water, Aron hung out for 127 hours in the canyon where a freak accident caused his right hand to be crushed under a boulder, trapping him. The only way to free himself was to amputate the crushed hand, which had no circulation and was no good to him anyway. He had a multitool knife. I know that knife, I have it myself. He first tried to chip away at the rock, but that didn't work. Eventually, he broke his own forearm bones, and with the dull blade, he was able to sever his wrist and free himself. Badass.
Some people think women can't be badasses. Obviously they don't know me, and especially don't know Jerri Nielsen Fitzgerald, who in 1999, operated on her own breast while stationed at a remote Antarctic scientific outpost providing medical care to about 40 scientists. Oh - this was during the Antarctic winter, with the last plane having left a few weeks before. Jerri discovered a small lump in her breast and operated on herself for a biopsy. The lump was cancerous, and Jerri removed her own breast cancer. Jerri died in 2009, after the cancer did reoccur. I'm sure she had better things to do in the next world, because if she hadn't, she probably would have wrestled the cancer down and told it to find some burly 300 lb. guy's man-boobs to infect instead.
Since we're talking cold-weather adventurers, Jerri might have gotten some inspiration from Ernest Shackleton, Irish-born explorer whose ship Endurance almost didn't have a name badass enough to stand up to his legend.
There are several excellent documentaries about Shackleton's Antarctic expedition, and one amazing dramatic film starring Kenneth Branagh.
Shackleton was the type of badass who recruited men for his 1914 Antarctic voyage with this advertisement:
Men wanted for hazardous journey. Small wages. Bitter cold. Long months of complete darkness. Constant danger. Safe return doubtful. Honour and recognition in case of success.
There is much to say, and know, about Ernest Shackleton, but after the Endurance became locked in Antarctic pack ice, it took 22 months, but he brought every man of his crew, and himself - home alive.

Here is a picture of Norman Ollestad, age 11, who survived a plane crash on Mt. Baldy that killed the pilot, his father, and his father's girlfriend. Norman got himself down the mountain one step at a time. His memoir of growing up with his adventurer father (the cover is a photo of Norman's dad surfing with a baby Norman slung on his back, surfing) and surviving the ordeal, is one of the best survival/personal stories of recent years.
First came Ernest Shackleton, who failed to reach the South Pole but who brought all 28 of his crew back alive. Then came Scott and Amundsen - one of the world's most famous tragedies, and the explorer who safely made it to the Pole and back. "I'm going for a walk; I may be some time," are the famous last words uttered by honorary Badass Mention Capt. Lawrence "Titus" Oates, who left Scott's tent during a blizzard, not wishing to burden his companions any longer. Then came Douglas Mawson, possibly one of the baddest of Antarctic badasses ever.
Here is Mawson telling the -40 degree weather it can take a hike and wait for him to finish his pipe.
In our winter/Antarctic "summer" of 1912, Mawson and a 25-man team of scientists and explorers set off to map and explore the coast and interior of Antarctica. Weather proved to be so harsh that the team was unable to make the 1200 miles of progress they had set as a goal. While trying to return to their base camp, their main pack sledge, all of its dogs, and its pilot, Belgrave Ninnis, fell into a glacial ice crevasse. This left Mawson and ski champion Xavier Mertz to continue on their own with minimal food. Eventually, the two began shooting their dogs for food, which continued for 10 days. Unbeknownst to the pair, they were being poisoned by excessive Vitamin A in the dogs' livers. Mertz's condition worsened, and he eventually died, leaving Mawson to continue alone. Struggling on, Mawson reached his base camp only six hours after the ship that had been scheduled to pick up the other men had departed. Holing up in their camp over the long Antarctic winter, Mawson and the others were eventually rescued more than 10 months later.