My opponent moves a unit into my battlefield with my unit. They then cast Ride the Wind before a showdown occurs. Is their unit designated an attacker or do they need to be in a showdown?

Yes — their unit becomes the Attacker, and there is no window for them to cast Ride the Wind before that happens. A Move is followed immediately by a Cleanup (Rule 455), and in that same Cleanup the Combat is staged and then opened (Rules 323.8, 323.12). Attacker/Defender designations are assigned the moment Combat opens (Rule 466.2.c), so the unit is already an Attacker by the time anyone can respond.

Their "before a showdown occurs" plan doesn't work because Ride the Wind is [Action] — playable on their turn or in a showdown's open state, not in a Closed State or as a reaction. The earliest legal moment after the move to cast it is inside the Combat Showdown itself, at which point the designation already exists and casting the spell doesn't change it.

If they do Ride the Wind the unit away mid-showdown, it loses the Attacker designation at the next Cleanup since it's no longer at the battlefield the Combat is at (Rule 323.2.c) — so any "while I am an attacker" bonuses, like Assault, fall off, but triggers that fired when the designation was gained have already happened.