You could do it, but temp control would be an issue.
I've got an old wood fire cook stove. It's got an oven and you can cook on top.
To bake in one of these old things you need to control the size of the fire, keep it fed and use the damper.
I think you would need something setup like that. A fire box with a damper and a cooking surface.
To me, the brew day is long enough without that.
Let's see if I keep this updated!
Black Butte clone
Up next.. Firestone Union Jack clone