If the furnace exhaust vent is a very low to the roof surface type it may very well have been incorrectly installed in the first place. Having this type on your roof is directly implied by your question regarding ice buildup on the roof.
For a more conventional furnace a through the roof furnace exhaust vent system is typical should have several key features as follows:
- A metal boot assembly that isolates any combustible building materials from the hot exhaust pipe.
- An extended stand pipe to raise the exit point of the hot exhaust exit well away from the nearby roof surface.
- A cap that is designed to prevent wind downdraft and rain an snow intrusion into the exhaust stack.
A high efficiency furnace uses a feature of a concentric piping system where the hot exhaust passes through the center pipe and prewarms the intake air in the outer pipe. Some other type of heat exchanger system may also be used.
The exhaust is also cooled so that at the exit the exhaust is composed of primarily water vapor and carbon dioxide. These components become acidic and must be properly managed. Because of the acidic nature of the exhaust the exit piping used is typically PVC and run through the sidewall of the house. Venting through the roof can be problematic and cause damage to roofing, especially metal parts.