If I conquer one battlefield and move to another to win, but my opponent uses Ride the Wind during my showdown to move to the battlefield I just conquered, do they win before I do?

Ruling: No, your opponent does not win before you. When you move to a battlefield and start a showdown, if your opponent uses Ride the Wind to move to another battlefield during that showdown, their showdown is "staged" and cannot begin until your current showdown ends. Since you win the game when your showdown resolves (assuming you win it), their staged showdown never gets to resolve.

Sequence:

• You move to a battlefield, starting a showdown
• Opponent uses Ride the Wind during your showdown to move to another battlefield
• Your showdown is already in progress; opponent's showdown is staged
• Your showdown resolves first
• If you win and score the final point, you win the game
• Opponent's staged showdown never begins because the game has ended

Nuances:

• To win by conquering, a player must score on all battlefields "this turn" - scoring one battlefield on your turn and another on your opponent's turn does not trigger the win condition
• A showdown cannot begin while another showdown is already in progress; the new showdown becomes "staged"
• When multiple showdowns are staged simultaneously (not when one is already in progress), the turn player chooses which staged showdown to resolve first
• An example of multiple staged showdowns would be in a 3-4 player game where multiple players use Ride the Wind to different battlefields at the same time