I can't answer that. Mine have never been near a bear or a lion. I suspect, though, that they'd be skittish at first but calm right down. That's what they normally do with anything new. Being near a predator might be different, though. I'd bet, though, that they'd deal with it better than a horse. They're calmer by nature.

“In a time of deceit telling the truth is a revolutionary act.”
― George Orwell

It's not over when you lose. It's over when you quit.