If the opponent attempts to conquer, then I ride the wind one of my units to an empty battlefield, which battlefield resolves first?

To determine which showdown resolves first when you play Ride the Wind to move a unit to an empty battlefield while another showdown is already in progress, the showdown that was already in progress always resolves first.

According to FAQ #2054, you must complete the current showdown before processing a showdown that is "staged" at another battlefield.

Sequence of Events

1. Current Showdown: The showdown currently in progress at the first battlefield must resolve completely (including its combat cleanup phase, where combat results are determined and control is established) before any other showdown can begin.
2. Staging the Second Showdown: When you play Ride the Wind to move a unit to an empty battlefield, you trigger a "Non-Combat Showdown" at that second location. Because a showdown is already in progress, this new showdown becomes "staged" and remains in a pending state.
3. Resolution Order:
   • The first (active) showdown completes all its steps.
   • Once the first showdown is finished, the second (staged) showdown begins.
4. Important Nuance: If the resolution of the first showdown results in you reaching your victory point total (8 points), the game ends immediately. In that case, the staged showdown at the second battlefield will never occur, as the game is already over.

Summary: The showdown that was already in progress when you played Ride the Wind always resolves first. The showdown created by moving the unit is "staged" and will only begin after the first one is entirely complete.

Note: I could not fully verify this ruling against the retrieved rules.