It's a terrible spell. Look if you see some equipment out there you want to destroy with an enchantment on it, people are just going to not risk the destruction spell until they have 4 extra mana, and then they won't have to worry about this spell at all. Plus, it costs the caster 6 points to force his opponent to spend 4 point extra to destroy it so you're not even getting an economic advantage. You've heard of throwing away good money after bad. This is the equivelent of throwing away good mana after bad. If the spell cost the opponent more than the 6 it cost the caster, then MAYBE it would be worth it. (still a weak spell since it can be planed for)
You're awfully confident about a card you've neither played, nor had played against you (or are you a playtester?). Armor Ward seems pretty similar to Suppression Cloak, and I haven't heard from anyone yet who thinks Supression Cloak is terrible.
If you're looking for a hard-counter, like in Magic the Gathering, obviously this isn't it. Mage Wars doesn't really have those (except, so far, Divine Intervention at 12 mana). But this spell doesn't seem any easier to play around than Nullify, and I think everyone agrees that Nulify is pretty great. After all, all you have to do to trigger a Nullify is play a Decoy on your opponent, and you'll get your mana back, too.
It's weird to me that you think people won't try to dissolve equipment unless they've got 4 spare mana, just because the opponent has a face down enchantment. Do you play around Nullify and Reverse Magic this carefully, too? There's a lot of things that enchantment could be, and you'll feel kinda silly if you let my face-down Bear's Strength prevent you from Dissolving my Lash of Hellfire.
You're right that the worst case scenario for Armor Ward is that the opponent guesses what it is, has the extra 4 mana to pay, and then never tries to Disolve any other equipment for the rest of the game. That's a 4 mana for 6 mana trade, and a loss of 1 action of tempo.
But that's not actually any worse than the worst case scenario for Nullify: the opponent guesses the Nullify, then doesn't cast any spells on the protected target. 2 to 0 mana trade, and loss of 1 action of tempo.