If Wolverine does the "dramatic jump over the camera while POV rotates to some goon getting chest impaled" move patented by Bryan Singer, I can see Logan losing.
However, this a 100-year old war veteran that has fought samurai power armor, a mutant with superhuman agility feats, a mutant with with nigh-superhuman agility feats that had the same adamantium skeleton as him at the time, his mutant step-brother that can swing the trunk of a tree like a baseball bat, and a mutant that can crush APC's and bust through walls by running into them.
Also, gotten crushed by logs and look like he just had a bad night's sleep when the logs on top of him are cleared, gotten shot hundreds of times escaping the Weapon X facility, gotten shot by like 50 arrows in the back and kept walking, survived an atom bomb, jumped off a nuclear power plant tower, thrown armored goons backwards over his shoulders like he was doing a double cable deltoid backhand, and survived having rebar twisting through him by Magneto then thrown into the Potomac River.
My argument is that if he can tank/survive this stuff and fight all these different opponents and still somehow come away with an action hero win, he can take down the Thrones crew.
EDIT: Inb4, "but the OP says no adamantium!" I know this, and yes obviously the adamantium made some of the above feats survivable for Logan. I still listed plenty of feats of Wolverine with just bone, and the adamantium wouldn't have stopped his organs from turning to mush and his tendons, ligaments, and fascia from snapping when doing something like jumping off the coolant tower on the nuclear power plant.