How an ice dam actually forms
The mechanism is well understood in building science and worth stating precisely, because the popular version of this story skips a step. Heat escapes from the living space into an under-insulated or poorly air-sealed attic, warming the underside of the roof deck unevenly — warmer near the ridge, colder at the eave overhang, which sits outside the heated envelope. Snow on the warmer section melts, runs down the roof, and refreezes the moment it reaches the cold overhang, building an ice ridge. Water continuing to melt above that ridge has nowhere to go but back up under the shingles, and from there into the attic.
PNNL's Building America program notes ice dams can form with as little as two inches of snow accumulation given the right attic conditions — this isn't a rare, extreme-weather phenomenon, it's a predictable consequence of heat loss meeting typical New England winter snow.

