I have one unit at a battlefield and I'm at 7 points. The opponent conquers the other battlefield and goes to 7 points too. He then comes on the battlefield I control with more might than me. I ride the Wind to the other battlefield and I have more might than him. Who wins?

Your opponent wins. Here's the sequence:

1. Opponent conquers Battlefield B → scores to 7 points.
2. Opponent moves into Battlefield A (where your unit is) → Combat Showdown opens at A.
3. You play Ride the Wind to move your unit from A to B. Since you left A with your only unit, your opponent is now the only player with units at A.
4. Showdown at A resolves first (per FAQ #9976 and #3278). Your opponent wins the combat, establishes control, and Conquers A — scoring their 8th point. They have now scored both battlefields this turn, so Rule 466.1.b.2 grants them the winning point.
5. Your staged showdown at B never begins — the game is already over.

Your unit moving to B creates a Non-Combat Showdown there, but it's "staged" and waits for A to finish. By the time A resolves, the opponent has already reached 8 points and won. It doesn't matter that you'd have more might at B — the game ends first.

This is directly covered by FAQ #3278. Opponent wins.