If water is leaking through the roof there could be other issues contributing to this problem...
You need to investigate your insulation!
Typically an insulation issue. Snow has an R-value of 1 per inch, this insulates the attic from the outdoors. Deep snow on the roof will hold in the heat loss in the attic and will begin to melt the bottom of the snow pile just above the shingles. When the water (melting snow) runs down the shingles and reaches a cold overhang it will begin to refreeze creating the "ice dam". The water table will increase as more snow melts and builds up behind the dam. Icicles form as water cascades over the dam increasing in height and length. If you have ice dams, the snow should be removed or separated from the ice dam. If this happens once, then you are more susceptible to it reoccurring again because the insulation has been compromised or damaged.
Ice Dam Cross Section - For a better understanding of how ice dams form.
Most roofs include Ice and Water shield protection. This is a rubber membrane that is waterproof and is installed under the shingles. However, when this is punctured with roofing nails that hold the shingles in place, it is no longer a waterproof system. If ice damming occurs, water could seep through it. It's designed to slow down leaks and protect the plywood from rotting.
"The roofing approach" to resolve ice damming is to ventilate your heat loss to the outdoors. This is NOT a good solution unless the attic is completely separated of any air loss from the living space. Isolate, and then insulate the attic from your home. In most cases the vented roof system will pull your (heated or air conditioned) air from your living space, i.e. recessed can lights, attic access doors, kitchen soffits, plumbing pipes and wire chases within the walls. The ridge vent is not designed to compensate for extreme heat loss due to insufficient insulation. Make sure your exit vents are not covered with snow, this will build up the heat in the attic.
An R value of 49 is required by current NYS building code for attic insulation. The effective R-value of fiberglass is only 2.5 per inch at its "best" performance. You would need 20" of fiberglass to achieve R-49 throughout the entire attic including near the overhangs. The area in the attic where insulation is the thinnest is usually over the exterior walls. This is the spot which contributes to the most heat loss and where the process of ice damming begins. Energy charts have efficiency ratings that can illustrate a drop in the performance of fiberglass up to 72% loss. This can result in an R-value of 1 per inch. Therefore, you would need 49" of fiberglass to get to R-49. These thicknesses can not be attained at the bottom edge of the roof deck. The result: lower R-values, snow melts and then you get ice dams. With High Density Spray Foam Insulation, you only need 3" to reach a 92% efficiency rating which is equivalent to R-50 of fiberglass. This thickness easily fits in the space at the bottom edge of any roof deck. The result: higher insulation efficiency, NO snow melt, NO ice dam, GUARANTEED we've seen it work for over 15 years.
You need to have a good air barrier and good insulation throughout the entire attic (no voids) and/or proper ventilation working effectively. A house with a deep snow blanket and no icicles is a well functioning system. We have monitored, studied and have been trained in the resolution and prevention of this occurrence. We have the product and technology to rectify these situations that cause ice damming. We will make recommendations to guarantee the solution to these issues.