This is a counter-intuitive, but it's the opposite.
As Valorum and Quentin posted sources to where it says he feels the pain and how he deals with it in this page:
And This YouTube video clip from one of the X-men movies
That answers the question partially, but leaves out a key thing:
Wolverine heals perfectly and completely which means he doesn't get caluses, thicker skin, deadened nerves, etc. that a normal human would do from repeated trauma to a given region of their body. The result of this is that Wolverine not only feels the pain at the level that a normal human would, he feels it worse in most cases than what a normal human would after having been hurt in the same way he does if they got hurt and waited to be healed to do it again, because their body has less nerves and such where as his does not.
On the other hand, there are many injuries that hurt not because they are in themselves painful, but because when you have them and move your body with them it hurts. For instance, you can break a bone and not even realize it until minutes later when you have to move the arm or leg and then you feel an excruciating amount of pain. With Wolverine, because he heals so fast he would likely not feel these injuries because he heals fast enough that the pain never kicks in.
So yes and then some, and also no. It depends on the circumstances. And you'd get really counter-intuitive situations if you started thinking about them. For example: Very hot fires won't hurt him at all, because the fire is hot enough to destroy his nerves, but lower heat fires would hurt worse because they're not destroying the nerves and you're always getting a fresh burn rather than a burn through charred skin.