I do both repair work as well as consultations on such problems. The problem with most suggested solutions is that they attempt to solve the symptomn & not the problem.
The usual suggestion is to add more insulation or more ventilation. The fact is that even a minimally insulated or ventilated attic should not have any significant snow melting above it, leading to ice problems. The reason for most such problems is convective heat loss (Air leakage from heated area to attics).
To solve the problem, structural areas where heated air can move direct into attic, as in: 1/ dropped soffits for cabinets (Many times the insulation has been installed suspended ove the soffits leaving a heated air pocket. If the soffit is on an interior wall, the wall cavities area added to the volume) 2/ Floors that extend into attic (usual solution is to put fiberglass to block. This doesn't work. A simple rule of thumb is that any material you can breath thru, won't stop air movement) 3/ Chimney chases that have not been flashed with an air-tight firestop at the ceiling line. 4/ Ceiling materials that are of themselves not air barriers with nothing else to stop air movement (as in T & G ceiling without poly or drywall above.
To solve, make these things as air-tight as possible. PAY ATTENTION TO DETAILS!