You can’t blame ppl for not shoveling on shabbos, im not a posek but i imagine that not everyone will permit it. (im sure mine doesn’t)
But whatever the case, ppl should definitely take precautions and shovel PRIOR to shabbos and salt.
If it snows ON shabbos usually that day its not slippery. Its at least the day after- which is SUNDAY, which hopefully ppl will shovel. But if you are talking about old snow that should be taken care of before.