If either were absent, the storm would have amounted to little or nothing. Among the oddities of weather science are that the coldest winters usually bring little snow. The reason is that moisture gets precipitated quickly out of extremely cold air. This is why, as people are surprised to learn, Antarctica is technically defined as a desert - because the extreme cold surrounding this continent prevents more than 10 inches of new snowfall from arriving each year. Conversely, the snowiest winters are often the warmest.
Snow comes from moisture in the air.
Moisture in the air comes from evaporation off ocean and lake surfaces, which requires warmth. Ice Ages, it used to be believed, came from rivers of ice called glaciers creeping south and covering the land. But now scientists assume that Ice Ages arrive from the sky, beginning with snows heavy enough to occupy parts of the landscape year-round. Such snow acts like a mirror, preventing the absorption of warming sunlight, thereby bringing more snow earlier in future winters. In 1816, with huge volcanic eruptions dirtying Earth's upper atmosphere and chilling the Northern Hemisphere beneath that shadow, snow remained around New England trees and boulders all year long, and summer brought ice and sleet storms as far south as the Carolinas.