As overnight temperatures fell to the 40s, power crews in more than a dozen states navigated a tangle of fallen trees, downed power lines and dangerous floodwaters in the painstaking, house-by-house work of reconnecting millions of customers left in the dark by Sandy.

Power was restored by late Thursday to about half of 10 million households and businesses that lost electricity during the storm, according to the Edison Electric Institute, a trade group that represents investor-owned utilities. But millions more remained cut...