Sorry, English isn't my first language.
I did some number crunching
Your first statement would have been false, IF at 45% cdr, nunu's old E cooldown was 3.6, animation and projectile speed that would happen casting an extra E would not make the 0.4 seconds difference in the gap between slows from the old E to the new E a nerf, BUT the numbers in your post were wrong, with 45% cdr old nunu's cooldown was 3.3 seconds, making the new one a nerf in that regard with the difference between cooldown and the slow ending being 0.1 seconds between the E's.
45% of 6, is 2.7 which is where the cooldown on old E was 3.3
Swift boost are of the same effectiveness because I got confused and forgot it affects strength and not duration, but the basic math is that % are more effective against longer duration CC because the cool down ratio between the two stays static , 20% reduction of 3 seconds, means old E was reduced to 2.4, while new E would be reduced to 1.6, a difference of 0.2 in reduction that would have stacked on the increased gap when the enemy is not slowed, if it wasn't so small after recalculation, would have actually made tenacity less effective against new E due to allowing a bigger gap to escape his range.
as it is, tenacity does affect his slow less, but not by enough to be significant due to the new numbers on cooldown
So you were right, but mostly because I put the wrong numbers when I did the math earlier, but in the end the nerf ends somewhere in the 0.1's of a second when it comes to duration of slows
the thing that has actually buffed is DPS in a lasting engage, because the damage reduction didn't actually cover the fact that he would cast one E more in the same time frame as old E, his new DPS actually exceeds his old by a lot.
To summarize, the duration and cooldown change together estimate to a insignificant nerf in consistent slow of around 0.1-0.2~ depends on the distance from the enemy.
but the changes to the cool down, over rode the nerfs to the damage and increased the damage out put but a large amount due to being able to throw snow balls at a 1.5 faster pace