Yes. Warm air inside your home can leak into the attic, warming the underside of your roof, causing snow and ice to melt, and then refreezing as it runs off your roof.
Ice dams not only indicate inadequate insulation, but they can also cause damage to the structure of the house. Heat escaping from the home through a poorly insulated attic warms the shingles on the roof, melting the snow, which runs down the roof to the eaves.
Since the eaves overhang the house and are cold, the melted snow freezes when it reaches the eaves; when enough ice has formed, it begins to stop or dam additional water from draining off the roof. The ice dams eventually grow under the shingles, causing melted snow to enter the ceiling and walls.