Peter Davison is at his absolute manic in Snakedance, starting this story at level ten and only getting more and more ferocious throughout the course of the story. It's a performance that's unlike any other that Davison gives as The Doctor, but it's absolutely electric to watch him.
Davison's Doctor has never been this quirky before, either. Look back at Episode One when Nyssa is reading aloud from a book about Manussa. Watch Davison completely steal the scene in behind Sarah Sutton, cautiously walking around her, noting with intense interest that something is different about his companion, then stares back to the corridor to try and trace her path. When Nyssa finally finishes, The Doctor finally hits twigs, "You look different!", noticing Nyssa's new costume. It's brilliant and hilarious.
Davison's manic turn in this story results in a remarkable event - we see The Doctor as others must surely see him: a crazed madman ranting about the end of the world while being dragged kicking and screaming. The Doctor does it often, mostly to the annoyance of Ambril. He's kicked out of the cave of the snake, he's thrown out of Ambril's office when pointing out Ambril's misinterpretation of a ceremonial headdress, and he really crosses the line when he bursts into Ambril's dinner party. Seeing The Doctor behave in this way, you almost begin to either distrust him, or, because of The Doctor's stellar reputation, make you think twice about every other raving lunatic you've seen do the exact same thing.