Pedestrians also tend to injure only themselves if they fall. Motorists can potentially kill many in one go. Including pedestrians. Think.
Schools have to remain open and kids have to be at them, on pain of sanction. Pensioners don't HAVE to go anywhere. Also, pensioners live everywhere, by definition: the school routes that are getting prioirity are only the immediate approaches. Think.
Gritting pavements would have to be done on foot, probably by hand, and the ability to have people on standby for this would be ruinously expensive, with council tax payers picking up the bill in a country where snowfalls of this severity are rare and people moaning about the size of council tax are depressingly common. Think.

Please, just think.

Piles of grit at streetcorners for hand distribution would in all likelihood be redeployed outside one mean-spirited person's door/gate/driveway within seconds. Frankly I trust the council more than I trust the ordinary citizen.