No messages needed. Since movement is already synced, the peer can just compare the host position to the previous position to see if the host is moving or not (in the air or not, ect), and play the correct animation. This gets a little trickier for attack animations though, depending on what you need.
Or just store host inputs as you would a peer's in an instance variable, and sync that. Then the peers would have the host inputs, albeit a little delayed, and can apply the proper animation based on input. This would be the most straightforward method.