If I am attempting to conquer on my turn and an opponent ride the wind over, are they attacker or defender?

In this scenario, you are the Attacker and your opponent is the Defender.

According to RiftJudge FAQ #9032 and Rule 442.1.a, the attacker and defender designations are determined by who first applied the "Contested" status to the battlefield.

Sequence of Events

1. Your Move: You move a unit to an empty (or uncontrolled) battlefield. This applies the Contested status to that battlefield, and you are the player who applied it.
2. Opponent's Response: During the resulting showdown, your opponent plays Ride the Wind to move their unit to that same battlefield.
3. Combat Begins: Because units from both players are now present, a combat showdown begins.
4. Designations:
   • You are the Attacker: You were the first to apply the Contested status to the battlefield (Rule 459.2.b.1).
   • Your opponent is the Defender: They are the player who did not apply the Contested status (Rule 459.2.b.2).

Important Nuances

• "Surprise Defense": This interaction is often referred to as a "surprise defense." Your opponent benefits from any "When I defend" triggered abilities on their units, while you benefit from any "When I attack" triggered abilities on yours.
• Conquering: If your opponent (the defender) wins the combat and has units remaining, they can conquer the battlefield and score a point, provided they have not already scored that battlefield during the current turn.
• Timing: The combat does not begin until the initial showdown concludes and the game transitions to the combat showdown (Rule 459.1).