I don't think stairs would end up being cleared of snow , the city would probably just close them as soon as the snow falls.
A short zig zag ramp up to the top would save about 100m of walking for people headed to the other side of the highway, and would probably be cleared, or at least be walkable in the winter.
Since the existing ramp is about 100m I'm assuming my example would require the same distance for that height of the bridge, but I don't know what the max gradient of walkways is.