The landlord. Definitely. 100% As the PROPERTY OWNER, the building's landlord must shovel the snow. Obviously, the building's superindendent or maintenace staff will do the shoveling. I would imagine that your landlord would not be out busting his hump with the shovel (unless he's a real good guy).
But, in the case of somebody slipping and falling on ice or snow, the property owner is the one liable to get sued, and that includes by his or her own tennants. So, when it snows, it's the landlord who needs to shovel and salt, including the stoop, steps, driveways, and/or the sidewalk adjacent to the building, up to where either the buidling ends or the next building begins.
City dweller, real estate guy.