Our house had a similar original design. Attached garage on the side of the house. They turned the garage into a family room, laundry room, half bath, and small bedroom, and then built another garage on the front of it.
I just saw an ad for salt tablets that you throw onto the edge of your roof to melt snow and ice. Don't know if they would work at these temps.
The room I am referring to was a self standing building about 12 ft. from the house. We added onto the back of the house to attach to that building. When thee were originally built (garage) they had no gutters.
If the gutters were clear of ice they would do a great job. If I get most of the 18" of snow off that roof we will be good to go.
They do make a heat tape for this issue I just never think about it until mother nature gets angry.....