A boiler is not a fireplace — it needs electricity. Circulators, burner controls, zone valves, and thermostats all run on line power, so a nor'easter outage stops even a perfect boiler cold. When power returns, most systems refire on their own; the ones that do not usually have a tripped control, a blown fuse on the transformer, or a circulator that seized during the outage.
The second storm effect is water. Low-lying Norwalk streets near the rivers and the Sound take on water in big coastal storms, and a basement that floods to the burner changes the job from repair to safety evaluation. If your street floods and the heat dies with it, lead with the flooding on the call — it reorders the entire triage. And after any outage, check that red emergency switch before anything else: it is the most common "dead boiler" in storm season.