Lowering Cooldown

If that doesn't answer it, I'm not sure what your question is either. Anyway, as the page says the cooldown is decreased by actual uses of a spell. So, any magic attacks used at all would decrease the cooldown as long as it's offensive magic, snapped or not. It says even blaze does it even though it can't be snap casted.

also, 3 topics down, in the discussion of blaze, this was fairly directly addressed since he asked the exact same question in that thread 11 months ago today.

No, it's not the "exact same"... This thread is asking if there's any condition in lowering snap cast's cooldown. That other thread didn't really address it; it just said incompatible spells lowered cooldown, not thoroughly explaining the function.

It might not be the same exact question, but it provides you with enough information to simulate the above scenario three times over. And what function is there to explain, exactly? You essentially asked a "yes or no" question.

And if you wish to be so technically correct, this thread does not ask "if there are any conditions"; it asks "is this specific condition a factor", which, again, can be answered through deduction using the information provided in the previously mentioned thread.