Can I use Ride the Wind on my opponent's turn to move a unit to a battlefield and get a point for it?

Yes, you can use Ride the Wind on your opponent's turn to move a unit to a battlefield and score a point, provided you meet the requirements for conquering that battlefield.

Ruling

According to the RiftJudge FAQ #1349 and FAQ #5614, you can use Ride the Wind during a showdown on your opponent's turn to move a unit into an open or contested battlefield. If you win the resulting combat or if the battlefield becomes uncontested after your move, you conquer the battlefield and score a point.

Why this works

1. Timing: Ride the Wind has the [Action] keyword. According to Rule 732.1.b, the Action keyword grants permission to play the card during showdowns, even when it is not your turn.
2. Scoring: You can score a point on a battlefield during your opponent's turn even if you have already scored on that same battlefield during your own turn, as scoring limits are per-player per-turn (FAQ #7138, FAQ #2364).
3. Showdown Mechanics: When you use Ride the Wind during an opponent's showdown to move a unit to a different battlefield, you trigger a new showdown at that location. This new showdown will resolve after the current one completes (FAQ #5614, FAQ #1895).

Sequence of Events

1. Your opponent moves a unit into a battlefield, triggering a showdown.
2. During your priority in that showdown, you play Ride the Wind (permitted by the [Action] keyword).
3. You move your unit to an open or contested battlefield.
4. The current showdown resolves.
5. A new showdown begins at the battlefield where you moved your unit.
6. If you win the combat or are the only player present at the end of that showdown, you conquer the battlefield and score a point.

Note: You cannot use this to score the 8th point (the final point) if it requires scoring from both battlefields in the same turn, as that specific victory condition requires scoring both in the same turn, not just just controlling them.