A possible reason why it is raining on Martha's Vineyard but snowing in Boston during this nor'easter is due to the specific heat of water and air. The ocean surrounding Martha's Vineyard is warmer than the air temperature, causing warm air to rise and cool as it moves over the water. This cooling effect leads to the formation of clouds, and as the water droplets within the clouds become too heavy to remain suspended, they fall as rain.
In contrast, cold air from the north is colliding with warm air from the south over Boston. As the warm air rises, it cools and forms snow instead of rain due to the lower specific heat of air compared to water. Additionally, the wind direction may also play a role in the difference in precipitation type between Martha's Vineyard and Boston. The wind direction may be bringing in colder air from the north to Boston, while Martha's Vineyard may be experiencing relatively milder winds.