Question about snare overlapFollow

Let's say I have Permafrost maxed and Improved Blizzard at 2 points. Both Cone of Cold and Blizzard would give a 60% snare. If I were to cast Blizzard on a mob already snared by Cone of Cold, would Blizzard's snare overwrite Cone of Cold's snare?

That's just the problem. >< If they had different values then there wouldn't be any question, but they're the same in this scenario.

If CoC remained, then Blizzard's duration would wear off through CoC's anyway, but if Blizzard overwrote it, I'd be left with a 4.5 second snare instead of CoC's vastly superior (and abusable) 11 seconds.