Lack of insulation causes heat to get dumped in the attic causing the roof to get warm and melt the snow which then runs down to the gutters which are un heated and then the water will freeze before it gets to the down spout assuming the ambient temperature is cold enough.

Lack of airflow alone will cause cold spots. You can actually see the overstuffed stud cavities the day after a light snow on alot of the old a framed houses.

No matter how much insulation you have the attic should be about the same as the ambient. The insulation blocks the heat transfer from the attic to the living space.