I have serious gutter issues on the front entrance to my house. There is a long flat overhang which is great a covered entrance. Keep my firewood there. But it’s a flat roof with no heat. when we get big snow, it just sits, freezes the gutter up resulting in icicles and ice on the walkway entering the house. Have an 80’ gutter heater cable which I plug into a thermostatic outlet plug so it runs when the temp is below 35f. Keeps the gutter clear, mostly. It’s a lifesaver.
see photo below. Heat loss is not the issue. The gutter is a good six feet from the house.