He would just freeze over and become a human Popsicle until found by a alien spacecraft or crashes into a planet. Could Wolverine survive crashing into Jupiter and not be crushed by gravity hmm?
He'd be stuck in space for two years tops (three if there are publishing delays) before someone finds him and thaws him out. Any more and a) sales would be hurt and b) the hack comic book writers of today would throw a hissy fit over not being able to rehash the same three or four fucking X-Men stories that Claremont wrote in the 80s.
And to think, non of this would've happen had DarkSydePhil's mom just bought the fucking Wolverine toy. Now that nigga is floating in space indefinitely. RIP.
Wolverine would just become brain dead from oxygen loss and slowly start to expire. The only way you can kill wolverine is destroying his brain by means of obliteration or immobilizing his brain receptors.
I'd say that he'd die eventually because he's run out of energy for his healing powers with no food. But these superhero powers don't follow energy conservation laws so some hack writer would probably just have him healing over and over and just floating around space forever.