In the episode a "Man without Honor" it's slightly ambiguous. When Theon threatens the inhabitants of Winterfell (I believe he says something like, "I told you something like this would happen if you disobeyed your lord") and then his men hoist up the burned bodies of the miller's sons, Theon looks really, really shocked, almost as scared as the castle's inhabitants.
My interpretation was that the men killed the children without his knowledge, and hoisted them up without his knowledge. If you actually watch the scene, he does not look as though he expected those burned bodies to be pulled up.
I really want to feel sorry for this guy. Not recognised as a Robb's brother, not recognised as his father's son. Neither a Stark nor a real Greyjoy, just a naive young man, trying to be respected. I want to feel sorry for him, but not if he burned two children.