If I control a Battlefield on my opponent's turn and then he conquers the Battlefield but then later in that same turn I ride the wind and re-conquer that same Battlefield, do I get a point?

Yes, you get a point.

According to FAQ #9424 and FAQ #2364, you can use Ride the Wind to move a unit to a battlefield, conquer it, and score a point, even if you already scored at that battlefield during your own turn. Scoring is tracked per-turn for each player, and the "once per battlefield per turn" restriction resets with each new turn.

Requirements for this to work:

1. You must lose control first: As established in FAQ #1067 and FAQ #9424, you cannot score if you maintain control of the battlefield throughout the entire showdown. You must have completely lost control of the battlefield to your opponent before you can re-conquer it.
2. The "Conquer" requirement: To score via Ride the Wind on your opponent's turn, you must successfully establish control of a battlefield that you did not control at the start of that specific combat/showdown.

Sequence:

1. Opponent's Turn: Your opponent moves a unit into your battlefield, triggering a showdown.
2. Loss of Control: You lose the showdown, and your opponent establishes control of the battlefield.
3. Your Opportunity: Once that showdown concludes (both players pass focus in a row without starting a new chain), the state becomes open.
4. Ride the Wind: You play Ride the Wind to move your unit into that battlefield, triggering a new showdown.
5. Resolution: If you win this new showdown, you establish control of the battlefield. Because the battlefield transitioned from your opponent's control to yours, you conquer it.
6. Scoring: Since you have not yet scored at that battlefield during this specific turn (the opponent's turn), you successfully score a point.

Important Nuance:

If this would be the final point of the game (the 8th point), you cannot score it unless you have already scored at every battlefield "this" turn. If you have not scored at all battlefields, you would draw an extra card instead of gaining the final point (FAQ #7467).