Yeah, this is weird. In my nearly 1,000 hours of gameplay, I've never seen animals climb ladders. Though, to be fair, I haven't set up an environment to test that specifically to say one way or the other. Clearly other people have seen it, though.
Regarding whether they should be able to is really just down to personal preference. Yes, some dogs are know to climb ladders IRL, but in those instances the ladder is not completely vertical like in-game. They're are a slight angle so it would be easier for the dog to climb. I highly doubt most dogs could climb a ladder that is straight up 90deg to the ground.