When snow melts higher up the roof and then travels down to the edges of the roof, it often refreezes just before it reaches the edge. The reason for this is because the eves of a roof are rarely insulated. No insulation means that the surface can be as cold as the air. As the ice accumulates, it builds a dam which holds melted snow back. The pooled water can seep under the roof's shingles and damage the underlying roofing materials. It can even leak all the way into the house and cause damage to ceilings and walls. Ice dams can be prevented by keeping hot air out of your attic. Colder climates should have a minimum of 1 foot of insulation on the floor of the attic.
As ice dams and icicles form at the edges of the roof, the weight can accumulate into a destructive force. You might not notice the damage until it's too late. This weight can bow your roof and pull entire sections off as the ice expands and contracts. Even if it looks pretty, remove it as soon as possible. If you have rain gutters that have filled with ice and have icicles hanging from them, the likelihood of the weight ripping the gutter off the roof is high. Gutters aren't designed to hold this kind of weight. Knock icicles down, and melt the ice by spraying it with a garden hose.
Icicles left to hang and grow on a roof tend to have a pointy end which can become extremely dangerous when it falls from the house. As temperatures rise, the ice can get soft and entire chunks can break free. Anything beneath these chunks can get damaged. A person or pet can be severely injured or killed by falling ice. Avoid these dangers by removing the icicles as soon as they form; don't let them grow. Keep all patio furniture or items that might get damaged out of the fall zone. If you have children, set rules to keep them away from fall zones.
If any exhaust vents on the roof become covered with ice, the carbon monoxide trying to get out will get trapped in the house. You can's smell this gas, and it kills people in their homes each year. Never allow ice to cover any of the exhausts on your roof. Snow is the culprit that most commonly plugs these vents, but unmanaged ice accumulations result from the snow. Remove the snow from your roof with a snow rake before it becomes a life threatening hazard.