You may target a tapped creature with Ice Floe’s activated ability.

The targeted creature is not removed from combat. Its attack will continue as normal.

If the ability resolves, then the creature gains flying later, Ice Floe’s effect will not end. (The ability checks whether the creature has flying only at the time you activate it and the time it resolves.)

If the affected creature is untapped by some other spell or ability, Ice Floe’s effect will not end. If you keep Ice Floe tapped, and that creature becomes tapped again, Ice Floe will continue to prevent it from being untapped during its controller’s untap step.

Ice Floe doesn’t track the creature’s controller. If the affected creature changes controllers, Ice Floe will prevent it from being untapped during its new controller’s untap step.

If Ice Floe untaps or leaves the battlefield, its effect will end. This has no immediate visible affect on the creature. (It doesn’t untap immediately, for example.) The creature will just untap as normal during its controller’s next untap step.