As far as classicness of non-animation, Trilogy client says:
Wolf movement (Ignore the laziness-induced sunk-into-the-floor aspect)
Werewolf movement
Not animating while ducking or jumping straight up is classic.
Wolf model should animate while walking, but keep in mind that the client switched to Luclin wolf models and stopped officially supporting classic wolf models long ago, and that animation triggers for movement are all client-side. Off the top of my head, it may be that the Luclin wolf model has a dedicated animation for walking, while the classic wolf just re-uses the run animation with a lower frame rate. When the client sees a wolf walking, it may be triggering the dedicated walk animation, seeing that it doesn't exist on the current (classic) model, and doing nothing instead.