Since I’ve been told by reputable sources that people don’t read (which makes me wonder why I’m typing this), here’s a recorded build guide for this weird monster.
If you want to see more, I’m streaming full playthroughs, endgame testing and uploading build guides in the above YouTube channel.
People are different 
Always prefer written guides, even if they are short, and videos only as showcase for SR, bosses and crucible.
Me too, I find them more convenient to search through/return to when needed, and I enjoy writing them. But since I now have this Youtube thing going, writing one seems redundant work I currently just don’t have time for 
I enjoyed watching some parts of your streams, you are a very good narrator in my opinion.
On topic of your build:
have you noticed pet speed is extremely low?, even for hybrid standards. So low it somewhat puts into question if they should be used. Have you also tried the build without the pets, if performance was better?
It’s not as low as it looks, the pets get affected by the % speed from Amatok’s Pact second node but it doesn’t show up on the pet UI. So they’re at like 30 % AS. Same thing with movement. Says they have 15%. Turn on Rallying Cry on GT. Still 15%. Lies and falsehoods. Same thing goes for pet % damage. There’s hundreds % cold on gear but the sheet only reflects % all damage, and there’s a bunch extra from buffs or item skill modifiers (like the one for Rallying Cry) that don’t show anywhere. The hounds are certainly not the star of the show, but they’re not entirely negligible. Even the fact they draw aggro, petrify with Korvaak and apply DR is a nice hidden boost to player survivability.
Either way, if you’re not using the pets, there’s zero reason to use Ice King. The whole allure of Ice King is the refreshable pets. Otherwise, you’re just cold werewolf that forgot its Fenris at home. There’s infinitely more merit to using Ice King as a full summoner build on some other mastery combo with no player damage than there is to use it without pets. Well, unless you’re a Reaver ofc, then you can’t have pets.
Edit: Forgot about Ice King’s Command proc, which has full uptime and gives pets another 12 % AS. So their real attack speed is increased by 42 %.