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Your boiler was likely installed in a space that does not provide sufficient combustion air.
The better and long-term solution is to provide a proper vent to provide the needed air. You seemed to have figured this out on your own.
The next logical question is where to put the vent and what size is needed.
I have always felt the answer to this question is not found in the law or 'code,' but what is safe.
The major concern to me is carbon monoxide production by the boiler. CO is made when there is not enough air to completely burn the gas the gas that is firing the flames.
The code seems a good place to find a 'safe' number for the amount of air needed.
The answer to what does the code say, is not easy to determine. There are a number of boilers in the US Boiler, Burnham Series 2 (Model B) product line. The difference is BTU input rating.
The install manual does not provide venting information, instead it points NFPA 54. NFPA states that JHA makes the final determination.
The NFPA answer requires knowledge of the furnace, and the amount of air in the house that can be used for combustion.
The amount of air, found through a formula based on measured or calculation of air provided by the house.
The issue of proper venting should also be addressed, this requires more, and different ventilation.
I know this did not give you a satisfying answer to your question. The CO issue is enough that you should have the needed changes made.
Best Answer
Scenario 1: Nothing. The heated exhaust air will melt its way through the snow and you won't have a problem.
Scenario 2: The furnace will malfunction. The exhaust pressure sensor will trip, causing an incomplete startup cycle.
Scenario 3: You'll get poisonous exhaust gases accumulating in your home, possibly causing illness or death.
Moral of the story: Make sure that doesn't happen by extending the pipes or whatever else is necessary. Make sure you understand how to do it properly so you don't make the problem worse.