We covered the wooden frame with chicken wire and stuffed it full of newspaper to give the "Great Stuff" spray foam a surface to stick to.
I went through a total of five cans of foam to cover most of the surface. Once the foam had cured, I began carving it with a fine-toothed pull saw.
So far, the effect looks pretty good. The marshmallow mountain slowly began to resemble rock as I cut away the smooth edges.
The next step will be to paint the surface with a latex primer and then airbrush in rock details with grey and brown. I'm still debating how to add the snow -- I may just sprinkle on snow rather than painting it to allow for more than one season's worth of use.