As far as who would win out, in no particular order...
Wolverine definitely has the skills in fighting, hunting, and survival. He could pretty much hunt down any of them eventually. Also his H2H skills allow him to go head to head with anyone. His biggest downfall will come coping with the loss of his healing factor. While yes he has been without it before, it still changes pretty much everything he does in a fight. He must be more precise.
Cap is the most out of his element since he is more of a straight up fighter. His enhanced attributes will play a big factor in his surviving. With his army survival training and experience, the terrain wont be much of a problem. His only real disadvantage is he is more of a straight up fighter than the others. He does not possess the stealth skills of many of the other fighters.
Hawkeye just doesnt seem to have much going for him here. He is a tough competitor but not much experience in these types of situations.
Castle could fair pretty well. This would not be all that different from his Vietnam experiences when it come to surviving. While not a great disadvantage to the others, Castle is a loner. He is used to being on his own with no help. He has the military know how and the tracking abilities to put him just below Wolverine in those terms.
Bats would do alright in this setting. He is highly versed in working in all sorts of terrain. He has great tracking skills and awesome survival training. His fighting skills allow him to stand toe to toe with anyone here. He could easily hide and mask his scent from others. He could set some great traps and surprise attacks. His big disadvantage is like other said, he would do everything not to kill the others.
Oliver has what it takes here. He went from spoiled rich kid to survivor and learned the hard way. He knows how to survive in this setting because he had to learn from first hand experience or he was a goner. His weapon of choice could easily be made in the wild by him, if he didnt aquire it first. He has the tracking, hunting, and stealth skills to carry him far here. His disadvantage is the amount of other characters with enhanced attributes. It puts him behind the 8 ball from the start.
Snake Eyes is a breed all his own. He is a highly trained ninja that is versed in all forms of weapons. He weapon of choice is a sword that in some instances, have cut a transformer. He has dodged bullets while in mid air. He also has amazing aim. His stealth skills will give him and edge considering it would be hard for even wolverine to hear him. Also he has all the survival training a ninja could ask for. I cant think of a real disadvantage for Snake-eyes since he has shown easily superhuman feats. He would personally be my choice to finish top 3 minimum.
Bucky has about the same going for him as Punisher except for the vietnam experience but he has his own that measures up. His bionic arm could cause quite a stir. If he connects with a punch with it, it could easily break bones. Couple that with his H2H skills and he is dangerous close up. He also has the weapons training to rival anyone here. His real disadvantage is he has less experience than the other fighters.