I can't speak to the materials used, but just a word of caution... If you're set on it being white, choose a material that's easy to clean (ie, NOT stucco). We prefer and have wood-burning fireplaces too, and no matter how careful you are, above the firebox will get some soot at some point. If you can just wipe it off regularly, you're good to go!

I've worried about that. Would plaster and cast stone fall into the same category as stucco?

I fear so. Any recs?

I think slate can be painted successfully, and a good paint would be easily cleanable.

Decorative - it doesn't appear to be used as a fireplace, but that is firebrick in most likely a usable firebox. Looks like a fine plaster finish or any fireproof material that can be sculpted to that shape.