Two different moths, two different winter habits
"Moth" covers a lot of ground, and the winter answer depends on which kind you mean. Outdoor moths — the ones that flutter around porch lights in summer — are seasonal. They lay eggs, the population declines with cold, and most species overwinter dormant as eggs, pupae, or occasionally adults in sheltered outdoor spots, largely invisible until spring.
The moths that matter for this question are the two indoor species: webbing and casemaking clothes moths, which feed on wool, silk, fur, and feathers, and the Indian meal moth, which feeds on stored dry food — flour, grain, cereal, dried fruit, pet food, birdseed. Neither of these species evolved to pause for a New Hampshire winter, because inside a heated structure, they've never had to.

