Can hidden cards only be played on conquered battlefields, and what happens to them if you lose control of the battlefield?

Ruling: Hidden cards can only be played to the battlefield you currently control. If you lose control of that battlefield, hidden cards go to trash.

Sequence:

• Play hidden cards only to battlefields you control
• If control is lost, hidden cards are sent to trash
• You can react by flipping a hidden unit before losing control (e.g., in response to a spell that would remove your unit)

Nuances:

• Cards hidden at a battlefield can only apply to objects in that battlefield
• Each battlefield has a Facedown Zone limited to 1 hidden card
• Zhonya is an exception: it can be played as gear onto your base, but otherwise behaves as hidden normally