Use black rubber stair treads, you can find them in most hardware stores at the start of the cold season. You simply put them down on each step, and store them away when the icy season has passed. No further installation required and no alteration of your stairs.
They are heavy and cling well to the steps, which allows you to shovel and scrape snow. Any amount of sunshine melts away what little ice and snow remains after shovelling. Even if some snow remains, it gets squished into the grooves when you walk on it, revealing the grippy top of the grooves.
Pick the good quality ones; they are thick, heavy and have long, deep diagonal grooves. Did I mention they are heavy?
PRO TIP: Don't assume that your steps are all the same length or depth! Make sure to measure EACH step in your stairs in order to pick the right size(s) of mats that will cover as much as the step as possible. For safety, you want the edge of the mat to line up with the edge of the step as closely as possible, and less than an inch for sure, other wise your foot will accidentally touch the unprotected edge of the step and it is a slipping hazard.
All this being said, with serious ice conditions, there is no solution to save you from an occasional shovelling, scraping or use of de-icing salt.