Depending on how “small” is defined, yes.
For the short-term ice-ages (individual Milankovitch Cycle-length, not the broader one that we are still in), at present, we don’t know many of the details about why one factor contributes more than another, but they correlate with periods of low orbital eccentricity, and/or low axial tilt. For the long-term ones (Cryogenian, late Ordovician, Carboniferous, Pleistocene, etc.), the main factors seem to be either a significant increase in atmospheric oxygen, and/or a concentration of continents near the poles.
Essentially, the issue isn’t so much “lots of snow” as “As a long-term average, there is more snow falling than melting”–the same sort of pattern, but in reverse, from what most glaciers are showing now.
In some cases, we have deposits from one at the bottom of a valley, then non-glacial deposits, then another round of glacial deposits, and so on. For the really long-term ones, it boils down to sequence stratigraphy: dropstones and glacial erratics in rocks in the local mountains in a few spots are in layers that are clearly beneath the ones where I am sitting, which are clearly beneath all of the coastal plain fossiliferous layers, which are clearly beneath layers relating to the most recent ice age.
That is simply a matter of definitions–are we talking about the “short”-term ones (tens of thousands of years) or long-term ones (millions to tens of millions).
Essentially, because it’s way too fast to be any of the ordinary cycles (similar magnitude of change to part of a cycle, but hundreds of times faster). Also, there’s nothing else going on that would cause that much of a change, besides the fact that people started releasing lots and lots of carbon dioxide into the atmosphere. Also, that carbon dioxide is old carbon dioxide–it’s isotopic ratios match oil or coal, not something recently alive.
