In a mild climate snow is an event and the roof shrugs it off within a day. Where it lies for weeks, the roof has a different job, and the trouble usually starts not with the weight of the snow but with the thin line of ice that forms along the eaves.
How an ice dam forms
Heat escaping from the house warms the roof deck above the living space. Snow on that part of the roof melts from underneath, and the water runs down the slope until it reaches the overhang, which sits outside the heated walls and stays below freezing. There it refreezes. Each day adds to the ridge of ice, and before long it is holding back a pool of meltwater with nowhere to go.
Tiles and slates shed water running downhill; they were never meant to hold it standing. The pooled water works back up under the courses and drips into the loft, often far from the eaves, so the first sign indoors can be a stain in the middle of a bedroom ceiling.
The damage you do not see in spring
A drip that ran for a few weeks in January soaks the insulation, and wet insulation stops insulating, which makes the next dam worse. The roof timbers and the boards above them stay damp well after the thaw. By early summer the underside of the deck can be furred with black growth, and the musty smell drifts down through the ceiling hatch. In places with long, snowy winters like western New York, homeowners have learned to have Buffalo attic mold experts look over the loft after a bad ice-dam season, because the growth is usually spread across far more of the deck than the original leak.
Stop the heat getting into the roof
The lasting fix is a cold roof. Seal the gaps where warm air leaks into the loft: the ceiling hatch, light fittings, pipe and cable holes, and the top of internal walls. Then bring the insulation up to a proper depth, kept clear of the eaves so air can still enter there.
Let the loft breathe
Ventilation carries away the little heat and moisture that still get through. Eaves vents feed cold air in low, and ridge or high-level vents let it out. If insulation has been packed into the eaves and blocked them, pull it back and fit rafter trays to hold the airway open.
Clearing snow safely
A roof rake used from the ground can pull the bottom metre of snow off the roof after heavy falls, which removes the meltwater supply before the dam can build. Never climb onto an icy roof, never chip at a dam with an axe, and never use salt on tiles. If a dam has already formed and water is coming in, warm water or a calcium chloride sock laid across the ice will cut a channel to let it drain until the weather turns.