Shiver Man's origins aren't completely clear, but it seems that he may have become who he is now after being cursed by a priest. Astonishing Tales #5 seems to show Shiver Man was once a man named Caleb Jackson who gunned down several armed men in a church, possibly seeking revenge for his wife, and then killed the priest, who cursed Caleb that he would walk the Earth forever for what he did that day.
In his first appearance he was hired to track down a fugitive who may have killed a senator. His involvement with Wolverine came at the request of Nick Fury, the only person who really knows anything about him. Wolverine was tagged for the senator's murder and Nick asked Shiver Man to find him. He walked into a diner and asked if anyone had seen the man in a photo he had. After some local men ridiculed his appearance, a waitress told them not to make fun of a burn victim. The local men told her to shut up and slapped another waitresses' rump. Shiver Man walked up to them and told them to apologize to her. When they refused and one man threw a punch at him, it passed through his body. When he phased through the next punch he blew off the man's hand. He then pulled out his guns and they decided to tell him where to find Wolverine. When he confronted Wolverine and the Beast he caught them completely by surprise. He ordered them to come with him quietly. They began to fight and Wolverine cut off Shiver Man's arm when he had to unphase to hold Beast down, but Shiver Man picked it back up seemingly unharmed and just left saying that he would return. They meet again later though, when Nick asks Shiver Man to trail an agent of SHIELD who was working for Weapon Plus. When he followed the agent to the location of the Weapon X project he realized Wolverine was innocent. He rescued Wolverine and an injured Beast who were being held there. The place was set to blow but Shiver Man went back in to take care of Sabretooth who was there too. The building exploded but Shiver Man walked out unharmed and hasn't been seen since. In Astonishing Tales is revealed he still works for Fury.
The Shiver Man has a wide array of powers. Assuming he is actually undead he does not need to eat, breathe, or sleep and may be immortal. He has an uncanny tracking ability with an indefinite range that may be magical or psionic. He has the ability to teleport, though it is unclear how far or how he can do this. He can transform his body into a mist-like form which allows him to levitate and phase through objects and people. When phaseing through people he can choose to harm them. He is incredibly stealthy, since he does not have a scent or heartbeat, even Wolverine could not detect him.
He also carries a pair of handguns that fire flaming bullets that might possibly be etheral or magical. But it is not clear whether these are actual guns or part of his body. When a victim is hit with a round from one, it continues to burn them internally.