I agree with your position.
Under "Stun" in the rulebook (pg. 32), it says: "A stunned hero in a zone does not count as being in that zone at all. The hero is effectively removed from the map for this round. "
Since the minions are not treated as being in that zone, "Ymir: Frost King" will not see that they are in his zone nor will they be included in any combat. "Ymir: Frost King's" "Always On" power shouldn't apply in this situation.
"Removing your finger. That's a good power, Uncle Glen. I must have it..."