My apologies to Fresh Codemonger, mineral oil will darken the steps and will leach back out over time showing the scratches from clearing the snow.
Use Muriatic acid to etch a new surface. I have had some success in removing most of the scratches in other slabs.
You will need to dilute it, apply it with a stiff bristle brush, use gloves and eye protection. It can be bad stuff, if handled improperly. Depending on the strength of the acid, I dilute 1 cup with about 2 gallons of water. I only suggest this as an example for dilution. As a caution, too strong of solution will yellow the stone or anything it gets on, besides burn real bad if it gets on your skin.
It will also need to be rinsed thoroughly.