Because of its location out at sea, Nantucket experiences a much milder climate than the nearby mainland. That's not to say that winters are pleasant and mild—indeed, they're not—but they generally are about 10% warmer than, say, Cape Cod. Nantucket is still subjected to fierce nor'easters, ocean-driven blizzards and mind-numbing cold.
Summers are not extreme either; cool ocean breezes keep average temperatures in the high 70s F/24 C, even in the middle of summer, although peak heat days can see temperatures in the 90s.
One thing to note is the prevalence of fog—Nantucket is not nicknamed The Grey Lady for its weathered architecture alone. Drifting in from the sea and hovering over the moors, the fog can appear and disappear just as suddenly, looking not unlike the setting for some Scottish mystery novel. As Mark Twain famously declared, "If you don't like the weather in New England, just wait a few minutes." This definitely applies to Nantucket.
More travelers than ever are avoiding the congestion of summer to enjoy the lingering warmth of both the winds and the water in September and early October. May and June are less crowded as well, but spring can be fickle and is later in its arrival on the island.