Frost Titan’s first ability affects each spell (including Aura spells), activated ability, and triggered ability that’s controlled by an opponent and that Frost Titan becomes a target of.

You may target any permanent with Frost Titan’s second ability. It’s okay if that permanent is already tapped.

If the permanent affected by Frost Titan’s second ability is untapped at the time that permanent’s controller’s next untap step begins, the last part of Frost Titan’s second ability has no effect.

If the permanent affected by Frost Titan’s second ability changes controllers before its old controller’s next untap step, Frost Titan’s second ability will prevent it from being untapped during its new controller’s next untap step.