An article in popular mechanics recently published about Ice Dam Prevention, and What to do if you have ice dam problems gets the basics:
To prevent an ice dam, don’t heat the roof, keep it cold. That way, the snow on the roof eventually dissipates without making large amounts of meltwater. The underside of the roof deck should not exceed 30 F. The best way to maintain low temperatures is by ensuring that there is adequate insulation and sealing gaps that let warm air pass into the attic from the house. The attic must also be ventilated, so that cold air is introduced into it and heated air escapes rapidly. Some remodeling contractors are under the impression that heat passing through the attic helps prevent ice dams, when just the opposite is true. Although excess heat moving from the attic through the roof rapidly melts snow, once the meltwater touches the cold eaves, it quickly freezes and forms an ice dam.
…Then the article falls short at really looking at solutions to identify root problems (other then proper insulation) and determining solutions. Instead it looks at situations where there’s a furnace in the attic, and then turns it’s focus to cosmetically hiding symptoms of ice dams. Before you go this route, you really should determine what the underlying problem is, and fix it.
If you don’t feel confident in attempting to diagnose and fix ice dam problems yourself, it’s always a good idea to contact a contractor that has a Minnesota State Certified Energy Auditor on staff, has experience in insulation & ventilation installs, fixing roof leaks and making stuff look good.