Many regions would be screwed. Necluda and Lanayru would be shut down, Hateno and Kakariko (whose economies are ruled by crops) would be screwed. Faron, Eldin, and Gerudo obviously wouldn't get snow, but if they did, Lurelin Bay would freeze over and the fish that rule its economy would decimate it. The Gorons wouldn't be affected too much; they've lived on Snowhead and Goron Mountain before. The Gerudo Desert being an ice desert, like Antarctica, would fix some things and screw up others. The Noble Pursuit would boom, the little girl's newly made Wildberry farm would be decimated. Kara Kara Bazaar would freeze over and the settlement would fall apart.
Akkala, the Great Plateau, Tabantha, Hebra, and the Ridgeland would be fine and probably wouldn't need to shut down ever (especially Hebra and the Great Plateau. Central Hyrule during its prime would have shut down pretty early on because horse-travel between, say, Mabe Village and Deya Village would be halted by the snow.