Does Deserter's Quarters get overriden by Horizon Boughs?

Question

In a game of Planechase, suppose we're on Horizon Boughs, which says:

All permanents untap during each player's untap step.

I have Deserter's Quarters out, tapped using its second ability to keep another creature tapped.

You may choose not to untap Deserter's Quarters during your untap step.

{6}, {T}: Tap target creature. It doesn't untap during its controller's untap step for as long as Deserter's Quarters remains tapped.

Would this mean I can choose not to untap Deserter's Quarters during the untap step, and keep the other creature tapped, or do both of them untap anyway?

Answer 1

Deserter's Quarters becomes next to useless.

If someone casts Burst of Energy targeting your Deserter's Quarters, it would untap since it's not your untap step. Same thing here.

When in Horizon Boughs, your Deserter's Quarters untaps in the other players' untap steps since you only have the option of not untapping him in your untap step. (The creature held in Deserter's Quarters remains tapped.)

Similarly, the creature held in Deserter's Quarters untaps in your untap step since Deserter's Quarters only prevents it from untapping in its controller's untap step.

Horizon Boughs makes Deserter's Quarters really inefficient. At best, you could retap a creature every turn for 6 mana in a two-player game.