I recently wrote a silly little flash fiction piece in which some party-goers go hide in a bunker under an apartment building in NYC because of a "megablizzard." In said silly flash fiction, I buried the Empire State Building up to its roof in snow in about two weeks. (In my imagination most of the North East is buried almost this high in snow, but not the far south of North America.) Now I'm curious if this is in anyway possible.
My questions are, in a world where snowstorms are gigantic and out of control and the winter never ends or goes above freezing, would this be feasible? Could NYC get so much snow that the Empire State was buried (to the roof: 381 m, not the tip)? How much snow would have to fall in what space of time to bury the Empire State Building to the top? And if so, what would happen to surrounding city? (I mean physically. Obviously everyone would be trapped. There'd be major panic. Transportation would cease. But would buildings be crushed and such?)