"I welcome it. The pasture is cleared of weeds and the wolves are frozen solid."
—Lumi, goatherd

Wall of Frost

Defender
Whenever this creature blocks a creature, that creature doesn't untap during its controller's next untap step.

The List

Modern Masters 2017

Defender
Whenever Wall of Frost blocks a creature, that creature doesn't untap during its controller's next untap step.

Planechase Anthology

"I have seen countless petty warmongers gaze on it for a time before turning away."
—Sarlena, paladin of the Northern Verge

Magic 2015

Defender (This creature can't attack.)
Whenever Wall of Frost blocks a creature, that creature doesn't untap during its controller's next untap step.

Magic 2014

If the creature isn’t tapped during its controller’s next untap step (perhaps because it was untapped by a spell), Wall of Frost’s ability has no effect at that time. It won’t try to keep the creature tapped on subsequent turns.

Wall of Frost’s ability tracks the creature, not the creature’s controller. That is, if the creature changes controllers before its first controller’s next untap step, then it won’t untap during its new controller’s next untap step.