My Rhode Island home is a north-facing property that rises above the sidewalk, built on an embankment. For scale purposes I'm including this fact; there are 17 steps from the sidewalk to the top of my porch, including 12 steps from sidewalk to the landing (this is the ground elevation), a 5 foot landing and then the final 5 steps to my porch. My home and yard get great southern exposure; but the sun does not touch my sidewalk, leaving it in shadow for most of the day during winter. Could a system of mirrors and/or lenses be effective in bringing light and the energy needed to help melt that snow?
Are trees or foliage part of this equation? Cutting back overhanging trees, even if it's not your first aesthetic choice, will improve our situation greatly. Another option is to put sidewalk heating systems into the surfaces, which will also dramatically improve the problem. Unfortunately, though, these systems can't be retrofitted. You'd have to reinstall sidewalks altogether.