That's either me misunderstanding what the thing does, or it's even worse than I thought!
No, you understanded that perfectly ...
In order to maximalize use of Mourning Frost (also, if they really want to make refference for Warcraft, why not make it a sword?) effect ...
You need party of 4 casters, of wich all (except the vielder) will use Frost spells ... and that debuff will give them +1 to damage per spell hit.
Sad story is that Frost spells are usualy weaker than their alternatives ...
Chromatic orb loose 1d8, when compared to Thunder version, or 1d8 + 2d4 (counting both turns of AoE, dismissing possibility to set enemy on fire, wich cause additional 2d4) when compared to Fire version.
So ... in order to get your 1 bonus damage ... you need to do at least 1d8 less damage. O_o
Not exactly atractive if you ask me.
Also, if all your 3 other party members will use Frost spells to gain that "sweet extra damage bonus" ... you get 3 extra damage ... if they all hit ofcourse.
Again, not exactly atractive.
And the best part?
IF you switch this super special cold radiating and cool looking staff for wich you needed to defeat three minibosses ... for simple branch you buyed from first vendor in game ... a Rain Dancer.

Your cold spells will do double damage to your targets for several (2 or 4? dont remember) turns.

So ... yeah, mourning frost is a shit item. :-/