Frozen condensate pipes are a common problem in extremely cold weather causing the boiler to fail. Thawing frozen condensate pipes is a tenant repairing obligation. If the pipe was not properly insulated or installed so that it sags or has an inadequate downward slope preventing water from draining, it is a landlord repairing obligation.
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Further Reading
Who is responsible for clearing a boiler condensate pipe? {Jungle Property Knowledgebase article}
How to Thaw and Prevent Frozen Condensate Pipes {Worcester Bosch}