should I sue?

Getting your municipality to change their policy would be the best way to go. The knowledge you have shown us about the condition of your roads, pretty much kills your suit.

Take a look at Quebec. To defer blame away from cities, and prevent lawsuits, they have made snowtires mandatory. Enough law suits, and then you WILL be buying those tires. Sorry, but I think you were at fault simply because you knew what to expect, and tried it anyways. Not saying I wouldn't have, but I would have taken the blame.