When I look at our zinc gutters with the current snow masses, I ask myself, how much snow or frozen snow can they hold?
At the same time, because of the sub-zero temperatures of the past few days, snow/ice is accumulating in the gutters and virtually nothing is sliding off the roof. Does an electric cable that you throw in the gutters and turn on when needed help? So that the snow always melts and slides down to the gutters? Or is the electricity supplier the only one happy with the fact that you are heating the outside air?
Snow is usually relatively light. Ice is even worse, and you'll be breeding it with gutter heating.
I know trace heaters from process plants, where they are designed to prevent closed pipelines from bursting with freezing media.
Sorry, but I can only describe this as an absolute joke idea :D
Re-fasten the gutter if it has fallen off.
Ideally, when you build them, you should make sure they have snow guards so the snow doesn't slide off the entire roof into the gutter and fall on someone's head below. Snow guards are relatively inexpensive if you install them, and much more expensive if you upgrade them.
I also think a heated gutter system is pretty silly. The gutter should be designed to fit the snow load zone, and there are extra reinforced gutters for mountains as well.
Cut off the long icicles. They do weigh quite a bit.
Snow bars or noses. Then you won't have to worry about someone getting hit by an avalanche from the roof.