Don't forget Man-Thing is immensely strong and has also defeated the Hulk, and between Swamp Thing's connection to the swamp and his ability to detect emotions I don't think Wolverine could sneak up on him there. Wolverine's MA and claws aren't going to do much here anyway.
When he is being sucked drowning into the swamp muck Wolverine will eventually know fear and start to burn. When that happens, his healing factor is going to make for a very long and painful experience as his flesh burns, his lungs fill with water and swamp turd, and he can't even scream any more.