What causes heavy snowfall in some winters and light snowfall in others?

Answer 1

It's basically the storm track, and the cause behind the shifting storm track is, as you can imagine, very complex. In addition to the storm track though would be factors that affect how strong a storm can become, which includes temperature gradients over both land and water (of the water itself). Also involved are accessibility to moisture for the snowfall, which has to do with the ability of that moisture to be transported out of source regions such as the Gulf of Mexico.

But at any rate, the factors that go into this are global in scale and climatologists can trace the causes back to what are called "low frequency oscillations" such as El Nino/La Nina, the North Atlantic Oscillation, and the Pacific North American teleconnection. These teleconnections operate on continental or hemispheric scales and affect weather almost everywhere. How exactly the work together to produce the given weather patterns that we see is an area of active research, and using them to predict the weather in the long-term is an art in itself.