It's freezing rain which, given the right conditions, freezes on the trees, and builds a thick coating of ice. Following the precipitation, it was windy which resulted in branches breaking off or trees toppling from the weight.
Much of New Hampshire is forested, so power lines were in great jeopardy throughout the state. There are still areas without power due to the damage. I didn't measure, but I'd say the ice coating was between 5 and 10 mm on many of the branches that came down.
Though New Hampshire got the worst of it by most measures, northern Massachusetts (bordering NH on the south) and Vermont (to the west) had extensive damage as well.