I believe we only have one owl, and it was just implemented in the show recently. Sorry to ruin any movie magic, but from what I've seen/heard, most of (if not all) animals featured in the Animal Actors show are just lookalikes. It's mostly all for show, in order to give the guests the impression that they're actually seeing the dog that was in How the Grinch Stole Christmas, Beverly Hills Chihuahua, etc. I highly doubt one of the owls used in the production of Harry Potter in the UK has been transferred to USH for an animal show. It's all convenient, really - add an owl to the show that looks like it came from a Potter film, mention that it was in the movies, and promote WWoHP all at once.
I digress. They could use any live owls in Hogsmeade if they wanted to, and it could all work out to their benefit since Animal Actors is right across from the entrance to Hogsmeade. I'm not sure if Japan considers that one of their unique elements, but it'd be cool to see here.