I would say that it definitely doesn't trigger
From the rulebook:
Example: The Spellweaver plays her Frost Armor
ability, which negates the next two sources of
damage against her. She places a character token
on the first circle of the card. Then each time
afterward that she normally would suﬀer 1 or
more points of damage, the bonus is applied,
the damage is negated, and the token is moved
forward one space.
If the null modifier is drawn, then you wouldn't suffer 1 or more points of damage. Also of interest - frost armor will negate damage from retaliate, traps, friendly fire, damage from re-rolling a short rest loss, etc.