Needlessly divisive?? It's literally one of the central issues guiding the project. Also, your last point makes no sense. Reassuring people that they'll be supported down the line as well, is a good thing.
Why does it matter if it is women and not men slipping on the sideways, and not just people? What if they now would find more men than women get injured because the roads are not cleared fast enough? Would they then reverse their decision? Or would women somehow still count more? Or what if the initial "analysis" would have found more people slipping on the sidewalks, but most of them being men?
Also the interpretation that it is "discrimination of women" seems dubious. After all, they are probably walking because they don't have to get to work, like the men (including the snowplough drivers). Then you are down to subjective values (not having to work vs slipping on ice and so on). Somehow people have forgotten that working is not an end in itself, but usually a means to support a family.
