Is it possible to draw a model partially (along the X, Y or Z axis) to make an extending barrier or something like that? (Scaling doesn't work because of the textures)
It is possible. There was a nice feature in XNA pre-4.0 called ClipPlanes. There are several good tutorials on how to use them, I'd recommend this one:
Now the problem is, ClipPlanes have been removed from XNA 4.0. Developers are supposed to implement it using shaders. I've found the following piece of code to do exactly this:
I didn't test it myself, but I hope it helps.