Heat inside isn't the entire reason for I&W. Ice can form on any roof whether it is heated or not.
The media has everyone thinking that all ice dams are created by lost heat, but it simply is not true.
On a shed, it is not required by code. All garages are required to have I&W from roof edge to 24" inside interior wall line.
It will really come down to which code they will use for your permit.
To settle an argument, check out the source. Look at the department of labor website and check the code.
In my area ice & water shield is required over all living spaces, pretty much the same as MJW, but over garages only if they are heated.Not here. Code doesn't even require ice/water on heated bldgs. Code only requires min 40# base at eaves and valleys. Of course code is always bare minimum, not industry standard which is what a decent roofer should follow anyways.
I am still of the opinion if it's not heated, it's not needed. Sorry but you are incorrect in saying ice dams are not caused by heat and freeze. Not trying to start anything MJW but can you give another scenario that will cause an ice dam other than the snow melting inside the interior wall and then freezing beyond the interior wall?
Well, I am trying to start something but it's not an argument.
Or water that hits metal (gutters, leafguards, valleys) and freezes because it is colder than the darker warmer shingles. That is usually how an ice dam initially starts.I have, on occasion, seen ice damming on unheated structures on the sunny side. As the roof is heated up by the sun, snow melts and re-freezes as runs into the shade. But, most ice damming problems are from interior heat loss.