The sweet thing about cooldown reductions is that it is based off of the original cooldown, not the current cooldown. In this case, it's a good thing that cooldown reduction is additive and not cumulative. 
Ok, I just for fun I tried this using TB equipped with a Vlemish, Magnus Rod, and Staff of Renewal. I was able to spam abilities nonstop with a slight loss of mana each time. Here's how it breaks down with ice TB maxed out on Cataract and constantly spamming spells. This is assuming your opponent decides to stay and play with Ice TB. I was too lazy to factor in casting time.
Opponent is constantly under Biting Chill.
Opponent is constantly under Rain of Ice's attack speed reduction.
Opponent is frozen 31% of the time.
Opponent is under Frost Nova speed reduction 51% of the time.
Opponent is under Deep Freeze cooldown increase 71% of the time.
Average DPS from constantly spamming Rain of Ice and Deep Freeze is higher.
This would be even crazier if Magnificent prescence was added. 