If a targeted creature is untapped at the time its controller's next untap step begins, the second part of the ability has no effect on it.

If an affected creature changes controllers before its previous controller's next untap step, this ability will prevent it from untapping during its new controller's next untap step.

You may target any two (or fewer) creatures. It's okay if any of them are already tapped. If you cast Permafrost Trap for , you don't have to target the green creature that entered under an opponent's control.