Yes, you can surely do it.
I get my foam from construction sites, but prefer 2" if I can find it.
I glue it together with lowtemp hot melt glue ( I use WS), because it is faster, but latex caulk holds a little better ( it may may take several days to dry between layers of foam.
I glue up piles of chunks - the key, make it too big, though pieces can be glued on later easily enough. Don't worry too much about holes, they make great caves or can be filled later. Ad castings if any when the basic shape is set. Just carve out a hole and glue the castings in. A little Drywall mud will fill the gaps.
I carve mostly with a steak knife. Key, carve too much, not too little. Don't be careful. I use a hot wire for hoodoos and a wire brush for finishing.
Know your geology, which way the layers run if any. Sedimetary rock will have straight parralal lines. These with be horizontal unless tilted or bent by plate tectonics. Sandstone, limestone, shale etc are examples as in the Grand Canyon or the Mississippi River Valley.
Volcanic upthrusts will be vertical by shape as in the Superstitions and Devils Tower.
A wire brush will add lines at the end of the carving.
If I have carved precise detail, I paint with artist acrylics, directly on the carved foam. For places where there is some weathering and dirt, I use my version of ground goop (Premixed light weight drywall seam compound, saw dust, latex paint for color, Lysol for mold and enough water to get the consistancy right. I paint it on with an old brush.
I then recarve and repaint until I like it or get bored.
To make a tunnel, make a stack and blast the hole with the steak knife, jusat like the prototype.
Expermentation is more useful than instruction, however I will be happy to expand on what I know if asked.
There are pics in my signiture, and though they are not neatly ordered, there ar a lot of process pics of the canyon and the mountains.