Chris Lewis writes:

On the contrary. Ice dams have _nothing_ to do with snow thickness,
and indeed, most ice dams occur with less snow rather than more.

If the eaves/attic is cold like it's supposed to be, you don't get ice
dams.

Nonsense.

The interior of the structure is above freezing, and assuming the
outside is below freezing, then somewhere in or around the structure, is
a boundary line between the two regions. Call this the freeze-thaw
boundary.

Whenever the freeze-thaw boundary moves out to the snow on the roof, you
get melting on the roof. Anywhere the melt runoff crosses the boundary
again, such as at an eave, refreezing will occur, and a dam will form.

Snow thickness definitely affects ice dam formation, because it affects
the motion of the freeze-thaw boundary, by virtue of its action as a
very effective insulator.

Do not confuse temperature with heat. Sub-freezing snow can very
effectively insulate heat that results in above-freezing temperatures.

No passive construction can avoid ice dams. Certain conditions will
always cause them. People are confused about this, because (1) they
don't know thermodynamics, (2) it depends on the weather pattern and
this varies, and (3) it depends on the type of construction which also
varies. Bad construction makes for bad ice dams, but that doesn't mean
the best construction can always avoid them.

Your error is in assuming the attic is always "cold like it's supposed
to be". Attics may be prematurely warm from poor insulation, but
eventually they all get warm from exterior heat. Eventually the weather
turns warm, and the freeze-thaw boundary moves out of the house and up
to the roof. When and how often this happens depends on the weather and
the quality of construction, but it does inevitably happen.

The only guarantee against ice dams is active removal, by heating or
mechanically or even chemically, which are all expensive and/or
impractical.

If you think ice dam control is simply a matter of proper construction,
then consider the Space Shuttle. $Billions and lives lost to a similar
type of ice formation, despite the concerted effort of the best minds to
avoid it.