We have this same situation. I do use ice melt on the step, but this year added a mat like this one and it’s made a huge difference. You might be able to find this type of material in a better shape/size for stairs.

https://www.hardwarestore.com/647554-grassworx-clean-machine-10372029-10254603-door-mat-30-in-l-18-in-w-rectangular-medium-flair-pattern-cinder