I think the central conflict is resolved when the rescuers from Poker Flat arrive and find Piney Woods and the Duchess in a death embrace. The text says that the people who found the two couldn't tell by looking which was the innocent and which was the sinner. (I am paraphrasing).
The point is, the people of Poker Flat had judged the two prostitutes, the gambler and the drunk as "undesirable" for their community. Nonetheless, most of the four outcasts were decent and even selfless, good people when given the opportunity. When they are faced with caring for themselves or caring for Piney or Tom, all except Uncle Billy take the higher path and give their all--even their lives--to protect the young couple.
So, even though they have died and seem to have lost, when the townsfolk from Poker Flat realize that they have judged the outcasts too quickly--that they are indeed good people, and that they are no better or worse (indistinguishable, in fact) from the innocents--then they win redemption. But the folks from Poker Flat changed as well. The implication is that they have learned not to judge too quickly or too harshly, and that the sacrifice of these outcasts will change the attitudes of an entire community. In their silence, the dead have gotten the last word.
For more information on themes and characters, see the links below.
Not all of the outcasts die; Tom Simson doesn't die and Uncle Billy's status is unknown since he leaves with the group's horses. The others, Mother Shipton, Duchess, Piney Woods, and John Oakhurst do die however. They die, but not before being able to redeem themselves. Mother Shipton, a madam, denies herself food so that it might be given to Piney. Duchess and Piney freeze to death, huddled together for warmth. While Duchess had been disagreeable before the group met up with Piney and Tom, who were eloping, afterward, she was tender and nurturing toward Piney and much more cheerful. John Oakhurst becomes the leader of the group when it becomes stranded. He sends Tom with a pair of quickly made snowshoes to Poker Flat to bring help. Oakhurst knew Tom had the best chance of making it to Poker Flat and that was the best chance any of them had of being rescued. Piney Woods died never knowing about the personal lives of the other group members and had no prejudice against them, so she died a young woman in love with no hatred in her heart.