This is trickier that it seems in a place subject frequently to snow and possibly ice. Simple glue-down non-stick strips with a surface like coarse sandpaper will easily get covered with packed snow or frozen rain / melted snow to a depth much thicker than the grit size of the strip. At that point it's just a film of ice or snow, WELL anchored to the stair step so that you cannot just scrape it off with a shovel! Even gritty paint has the same problem. About the only way left to clean it off after shovel scraping is to use ice-melting salt followed hours later by a broom to sweep away the slush it makes so you're back down to dry grit. And that won't work when it is really cold.
Sometimes a better solution actually is to ensure the surface is flat and NOT really rough, so that ice and snow will not bond well to it and you can effectively remove it with a shovel and broom. Unfortunately, bare wood, or wood treated with a penetrating stain, still provides a good surface for water penetration and bonding. A good outdoor tough paint, or perhaps a silicone water-repellent treatment, may help reduce the ability of water and ice to bond to the wood.
Then there's the industrial solution - expanded metal grating with lots of holes and sharp upturned points.