Flashing around the stove vent may have become loose or damaged, creating a gap that allows water through. Water could be penetrating through the roof around the stove vent if the ice or moisture in the exact area of the gap melts or if heat from the stove vent or other warmth has led to the formation of an ice dam. An ice dam forms as the result of warmer roof temperatures that cause snow to melt and run down the surface of the roof until it reaches a colder area and refreezes. Unfrozen melt backs up behind this ice and the standing water is able to penetrate roofing materials.
Provide immediate relief for the leak by removing as much snow as possible from the area surrounding the stove vent. Use a roof rake, a long-handled tool specifically designed for this task to rake snow down the roof. In some situations, snow removal alone may provide adequate immediate relief. Otherwise, inspect the interior of the roof in the attic. Warm air leaking through any gap around the vent pipe can lead to melt and an ice dam, so seal any spaces around the vent and framing that allow air or moisture passage with a high-temperature sealant.
Make warm weather repairs once snow and ice have disappeared from the roof and the roof work can be done safely. The flashing or storm collar around the stove vent may have come loose and allowed the leak. Replace flashing if it is not properly-sized or has corroded and reattach flashing and the storm collar. Ensure that both are securely attached and seal these protective devices to the roof with flashing cement or asphalt roofing cement.
Increase the amount and quality of insulation in the attic and around pipes to lower the attic temperature and prevent or limit the formation of ice dams. Seal cracks or spaces in the attic floor from the ceiling below or where wiring or pipes penetrate the attic floor with spray foam insulation. Use a non-combustible insulation like mineral wool that can tolerate high temperatures around any hot pipes.