Icy sidewalks are a dangerous liability to you and your guests. Melting snow can also cause ice dams that trap water on your roof until it seeps into your attic and down your walls. Ideally, this problem can be cured by additional insulation in your attic, or possibly more ventilation.
Heat cables are an option in those tough situations that defy other solutions. They will melt a path for water run-off all the way through your gutter system, preventing water back up and icicles.