If I cast aether snap removing all counters from Yorvo, Lord of Garenbring, it dies because the counters are removed and he becomes a 0/0, right?
Assuming Yorvo isn't a token, yes, since its toughness becomes 0 once its counters are removed, and nothing else is affecting Yorvo's toughness.
If Aether Snap removes counters from a nontoken creature, check the creature's power and toughness (without the counters) to see what results it would have. In general, a creature whose toughness becomes 0 or less will die as a state-based action (compare Yorvo with Wayfaring Temple).
If Aether Snap removes counters from a nontoken creature, check the creature's power and toughness (without the counters) to see what results it would have. In general, a creature whose toughness becomes 0 or less will die as a state-based action (compare Yorvo with Wayfaring Temple).
EDIT (Jul. 2): Correctness edit.