More snow means more of the planet covered in sheets of blinding white. More white means more sun heat reflected back into space. More reflected heat means more cold. More cold means more snow.
That's Gaia doing her magic. Is this how ice ages begin? Global cooling? Sounds reasonable to me, although I'm the first to admit climate isn't my field of science.
This New York Times article by Judah Cohen has one explanation, somewhat convoluted and forced.