According to answers on the wowtcg.com forums, War Stomp triggers in two different places, depending on whether the character with War Stomp is attacking or defending.
If attacking, then War Stomp triggers at the beginning of the Attack Window, just after the attacker exhausts for that attack.
Since this happens before the Protect Point, you can exhaust a protector before they can protect with it.
If defending, then War Stomp triggers at the beginning of the Defend Window, just after the Protect Point.
You cannot use War Stomp while defending to stop the current attack, but you can exhaust another character to stop them from attacking that turn."
The upshot of this is that when you are attacked by an ally with War Stomp, the attacker can exhaust your hero before the Protect Point, when you are still just the proposed defender. Since you're not yet the defender, you can't respond by exhausting your hero to pay Frost Trap's cost.