As a powerful blizzard blankets the East Coast in snow, another force of nature is preparing to take over the chilly streets of Manhattan. Los Angeles-based singer-songwriter Gaby Moreno will make her Broadway debut as Persephone, one of the leading ladies of Anaïs Mitchell’s Tony Award-winning musical “Hadestown,” beginning Tuesday at the Walter Kerr Theatre in New York City. Exploring themes of climate change to a New Orleans jazz- and American folk-laden soundtrack, “Hadestown” — a retelling of the Greek myths of Hades and Persephone, as well as Orpheus and Eurydice — will open just as New York transitions out of the harsh winter. Moreno, 44, takes a video call from The Times during her second day of rehearsals, as she is learning how to play Persephone, goddess of spring — and in this play, a wine-drunk lush. “For the first few minutes I was like, ‘Can I do this? I feel like a klutz,’” she says of her character’s flailing steps, meant to distinguish the inebriated goddess, who splits her time between the underworld …