[Ugly Joe]

Just another couple cents worth...

Depending on what the glue's going to be exposed to, might dictate what adhesive you'll want to go with.

One thing about Gorilla Glue (and other polyurethane glues) is that it makes a stiff foam - it can be carved and sanded, like a hard foam.
If you're going to be using this where you may have to cut through or carve through the glue layer, I think you'll pull out less hair using Gorilla Glue.

Flip side of that coin is: it doesn't seem to take the elements for more than a season or two, if it's not thoroughly sealed against moisture.
(I've used Gorilla Glue on my countdown sign, without being sealed, and it gave way after 2 seasons of nightly moisture...but the stuff I've had covered with paint is still holding fast, even with similar amounts of exposure)

Liquid Nails is great if moisture will be getting to the glue...and it holds foam together - both the styro as well as the extruded.
Sadly, it's hard to cut and shape...so if it's in the way of your carving, you'll need to work around it.

 

[Ugly Joe]

And here is my sketch of how I want to build my new 2009 Cider Shack. The roof section will be build from 1" Expanded Polystyrene foam sheets.

Shweet!! Yeah, that Hazlewood Manor facade is a real inspiration - that will be a NICE setup for your cider shack.
Are you going to put anything inside the roof, to show through the windows?
Thoughts of moving shadows...or eyes lighting up. Like evil little red eyes glowing out at people through a dusty, clouded, ancient window.