Salt doesn't keep roads ice free when it gets too cold, it works in warmer climates but in Sweden it gets cold enough that you will have ice patches anyway. They would stay a shorter period, but they would still be there, so cars still need winter tires so they can drive on ice anyway, so can just as well not put toxic salt on the roads.

People who slip mostly just needs better shoes/tires, the difference between good and bad shoes/tires is huge. I have biked in Sweden during the winter, no problems at all, winter tires fixes most issues.