Buh, I dunno, whenever I fight my dog, he power attacks with a greatsword, but he's a munchkin anyway.
I suppose you're asking if animals have handedness like people; I would think so, they have separate hemispheres of the brain just like people.
Note that handedness penalties only apply in D&D if you're fighting with two weapons; there is no rule for handedness. If you are fighting with a one-handed weapon and nothing else, you can do it with either hand, strictly by the rules. Many people house-rule that if your character uses his nondominant hand he takes the off-handed penalty.