I hope I can adequately describe what we did to our 5er steps:
I had a 2' x 6'(+/-) strip of astroturf, that I clipped to the top step with some small spring clips attached at the back. I draped it down the steps, then used a few pieces of thin threaded rod placed at the inside corner of each step (it kept the carpet from shifting). The rod was wider than the steps, so "locked" behind the edges of the steps. And clamped the bottom of the carpet to the bottom step. Was nice and secure, non-slip, and for my dogs, gave a "solid" appearance to the steps so they were less spooky about climbing them.
If the carpet got muddy or snowy, unclipping it and shaking it out was easy.