My dog showed a fear of walking on grates, the kind they sometimes have on the sidewalk for storm sewers. He would run to the end of his leash and try to run around, sometimes into the street, or plant his feet and refuse to go over.
Basically I ended up having him walk over every grate on our walks, luring him onto them with treats and having a celebration for every step he would take. By the end of the week we were walking over grates with only a look at the ground.
Is it just specific spots? Or is he refusing to walk on the hardwood at all. If it's the hardwood as a whole I would reward him for stepping from one surface to the other. If it just specific spots, I would just try and take your time and encourage him through those spots with happy words and snacks. And a tight leash so he can't get away. If you can make him face his fears and make it a positive experience he should get over it quickly.