hi! if you can specify which region/culture you're interested in, that will assist the appropriate historians to find relevant answers. In the mean time, here are some previous responses to get you started:
In addition to the earlier references, realize that a primary concern with snow removal today is in vehicle safety. Automobiles travelling at 100 kph don't generally track well in snow and ice.
In an age prior to motorized transport, when you got around by walking, by draft animal (horses, donkeys, oxen), or by sled, there was far less of a need to clear all snow. You'd still need to shovel clear building entrances, etc.
But the problem domain was different.