Yes, they can. All this ******** about 'being sued' is a myth designed to abrogate responsibility for people/businesses too lazy to do anything. The facts are that you can clear ice and snow providing you use common sense. So long as you're not throwing hot water on it to melt it or something equally as stupid, you're not going to get sued. If someone suddenly decides to stop taking care because they see a clearer patch of pavement, that's their fault, not yours. Anyone telling you otherwise is simply too lazy to leave their warm office/cozy armchair and go out into the cold.
Absolutely baffles my missus that folk here don't bother clearing the pavement outside their house. If everyone just did there part (and mucked in to help out the elderly/disabled) it would be a hell of a lot better.
To be fair though, she probably thinks we should blast it away with the high calibre sub machine guns she thinks we should have in the cellar...