Terrain can make a difference. If given the choice, I'd walk over ice that was on top of grass, gravel, or smaller stones (that is, most are in the 1-3" diameter range) over concrete or asphalt. That ice generally gives way under you and provides you a chance to get traction without specialty footgear. The ice that forms on pavement is often much slicker, and the pavement doesn't give so the ice doesn't break underfoot.

Concrete and asphalt also promote the development of ice in a way that other surfaces do not, because they retain heat from the sun hitting them. That's the principle issue here, even when it's 10-20F, the pavement is easily above freezing on a sunny day, and when the snow falls in the afternoon it quickly melts and refreeze creating hazardous conditions until the next day when it thaws (assuming it's not a deep snow) as the sun hits it again.

Or walk on the snow rather than the ice.

How common were perfectly manicured sidewalks back then?

Our snow is not very deep here, normally. At least not in the winters I’ve been in. But yes, prefer snow to icy patches if it’s an option.