An ice dam on your roof can result in water sneaking under roof shingles and eventually reaching interior walls. Look for wet spots or streaks of dripping water where the ceiling meets a wall.
Ice dams usually result after extended periods of snow and cold but can occur after a just a single snowstorm where the snow/hail is blown against dormers or intersections of rooflines where water can intrude.
Removing an ice dam from the roof can be simple or difficult depending upon its location. Sometimes the issue resolves itself after a warm day. A slightly damp wall is not a major problem; it will dry nicely. A soaked one, however, will need to be replaced.