I have a hidden Tornado Warrior and a Steel Paws on a battlefield. My opponent attacks that battlefield and passes priority. I play the Tornado Warrior from Hidden as response, targeting Steel Paws as my empower target and pass priority. My opponent plays gust on the Tornado Warrior in response. Does the Steel Paws still get empowered?

Yes — Steel Paws still gets empowered.

Your play-from-hidden trigger was already placed on the Chain with its choice locked in when you targeted Steel Paws (choices for triggers are made at finalization — Rules 383.3.a, 402.2). Gust only bounces Tornado Warrior; it doesn't counter the trigger, and a triggered ability already on the Chain resolves independently of whether its source is still on the board. When the trigger resolves, Steel Paws becomes Empowered (assuming it's still there and wasn't already Empowered — Rule 441.1.c).

Also, the "disempower it at end of turn" is a Delayed Ability that fires at end of turn regardless of Tornado Warrior now being in your hand (Rule 392), so Steel Paws' +7 [M] from its Empowered ability lasts only until then anyway.