Ever read What If? Spider-Man Vs. Wolverine Vol 1 #1
The whole story concerns Spider-man joining up with Wolverine to terminate terrorist organizations after he accidentally killed a KGB friend of Wolverine's (in the main universe he was haunted and horrified and went into Mary Jane's open arms. In this universe he "stayed in the cold"). He becomes a better martial artist and assassin than Wolverine and he develops his spider sense to the point that it's actual precognition (to the point of detecting things hours and days ahead if I'm remember correctly).
His outfit was really awesome too: