An AT-AT strikes against a Hoth objective, but uses its ability to remove the Subzero Defenses enhancement instead of getting the icons. Is the AT-AT still destroyed?

I don't think so. The key is "after its strike resolves" on SZD - at that point, SZD has already been destroyed and thus no longer applies.

I concur. Timing-wise, you can think of SZD's text as an immediate forced reaction. Since the strike fully resolves first, SZD is out of play before its reaction could trigger.

Edit: Typo...

Reaction: After this unit is focused to strike, instead of resolving its combat icons, discard a target non-limited enhancement from play.

Destroy the first enemy unit to strike against a friendly Hoth objective each turn, after its strike resolves.

The Way I read these, when the AT-AT goes to resolve its icons, you can sac an enhancement, so the Sub0 defenses happens AFTER the strike resolves, at which point the enhancement is already gone.

this has already been answered over on card game DB in the official rules thread.

it is as everyone saw it, AT-AT kills sub zero defenses before it kills AT-AT