If the accumulation of snow is left on a roof too long and the temperature stays very cold the snow is melted from underneath (the attic) and refreezes as it goes to the lower area of the roof at the soffit. When enough ice has formed at the soffit it begins to dam the water from going off the roof-it then backs up and under a roof shingles causing the water to enter your home.
Some Preventative Measure:
Get the snow off your roof in a major snow storm. The sooner you do this the less ice will have formed and if done by a professional roofing contractor the less damage to the roof will result.
Check for air leaks into the attic area - one of the most common is an attic stairway that has warped and is allowing the hot air to enter your attic. Make it air tight.
The vent from your attic fan- If it does not shut correctly will allow air also to pass into the attic- cover that opening from above with a blanket of insulation that can be removed in the summer months. Most of these fans have an exhaust vent on the gable of the house -if the vent is in the closed position you have lost the cross ventilation of your attic. Screen the vent and make the louvers stay in a semi open position.
Check for proper attic ventilation - the screens on the gable vents will clog with dust after years and should be cleaned- the cfm's (cubic foot a minute) will have been decreased from the clogged screen and contain the heat buildup in the attic. A simple whisk broom will do the job.
Another common air leak into the attic is an exhaust fan from your kitchen or bathroom that has not been vented through the attic and out the roof, but just vents into the attic. Check the insulation in you attic: One of the best ways to tell if your attic is too warm is to notice if your home gets a lot of icicles in the winter (icicles come from melted snow)!!!! In a real bad storm the newer homes that are built with updated building codes will have fewer icicles than the older homes with less insulation and inadequate ventilation.
If you still feel you need the advice of an expert call your professional roofing contractor and ask him to take a look at your home. New roof or old roof under blizzard or like conditions get the snow off the roof. Roofers build roofs, not swimming pool liners - they are not designed to hold water, nor will they.
There are other measures that your roofing contractor will be able to offer you to help decrease the chances of Ice and Water backing up into your home.