Carpet wraps worked for our black lab, too.
I also discovered that he didn't like being able to see 'through' the steps, due to their open backs. Though the steps must be folded for travel, the solution was an easy one. We got a piece of lightweight outdoor carpet, and attached springs to all four corners. The springs attached to the top and bottom steps from the underside, and don't interfere with human traffic. Easy on, easy off, and the dog see 'solid' steps.
2016 Coachman Leprechaun, 319DS, Motorhome, Dodge Durango Toad