When this creature transforms into Awoken Horror, return all non-Horror creatures to their owners' hands.
For more information on double-faced cards, see the Shadows over Innistrad mechanics article (http://magic.wizards.com/en/articles/archive/feature/shadows-over-innistrad-mechanics).
Removing all ice counters from Thing in the Ice some other way will not cause it to transform. You’ll need to cast an instant or sorcery spell and cause its last ability to trigger.
When Thing in the Ice’s triggered ability removes the last counter from it, Awoken Horror’s ability will trigger and resolve before the spell that caused Thing in the Ice’s last ability to trigger.