Many people think that if a building owner shovels and salts the sidewalk in front of his building, then he cannot be held responsible if you slip and fall and are injured. Nothing could be further from the truth. Many times a landlord makes the situation worse by the way in which he or she shovels the snow by leaving it in piles or creating chunks of ice.
The law in NY holds that even if a landlord removes snow and ice, if it is made more dangerous because of the shoveling then you may bring a law suit against the landlord. And, of course if the landlord does nothing to remove the snow and ice then he or she can be held responsible for that also.
If you have been injured by falling due to snow and ice then you should consult with a personal injury attorney who will discuss your case free of charge.