Freyalise's Winds

During your untap step, first you determine which of your permanents will untap, then you untap them. If you control a permanent that says “You may choose not to untap [this permanent] during your untap step” and you decide not to untap it, no wind counters will be removed from it because it wouldn’t untap. The same is true for a permanent you control that wouldn’t untap due to a spell or ability (such as the one from Barl’s Cage).