If my opponent moves my unit to their battlefield causing a showdown, and I use Ride the Wind to move it back to my empty battlefield during that showdown, do I score a point for conquering that battlefield even though it's my opponent's turn?

Ruling: Yes, you will score a point for conquering the battlefield, but not immediately.

Sequence:

• After your unit is moved to the opponent's battlefield, a showdown starts there first
• That showdown continues even after you move your unit away with Ride the Wind
• After that showdown finishes (both players pass focus in a row without playing an action), a second showdown starts on the other battlefield since your unit is on an uncontrolled battlefield there
• Once that second showdown finishes, you will score a point (assuming the unit is still at the battlefield at the end)