Now it's possible thanks to the Middle Earth Digital Elevation Model Project. It's still a project in progress, but what they've created so far is pretty amazing.
What's more, they're working from Tolkien's texts, both finished and unfinished, as well as his notes, and not so much (at least from what I've read) from the movies.
For those of us who are slightly more technically minded, it's even possible to download a simulation of what they've created so far. Personally, I'm not quite game, at least not right now, but I definitely like some of the videos they've made available as well.
I'm definitely impressed!