Try using cracked feed corn on slippery sidewalks instead of salt. It doesn't damage your lawns and it provides food for the birds. It's very reasonably price, too, about seven dollars for fifty pounds at any feed store. Granular fertilizer also works if you don't have access to feed corn.
Granualr fertilizer on paths is a bad idea. When the thaw comes the fertilizer will be washed into stormwater drains and thence into river systems. The wash off from lawns and gardens is bad enough, causing overload of nutrient in waterways and blooms of poisonous blue-green algae, without adding to it.
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