Cold sorceress: HOTO vs Doom

Neither.

Up front, the real answer would be "doesn't matter" as cold sorc for most people means blizz sorc and blizz dmg once somewhat geared is so stupidly high that even un-optimized, you just annihilate nearly everything on P8 (including cold immunes).
The CI nerf was more of a massive nerf to other cold builds (cuz those were apparently too strong, what with 0 people playing them and all), rather than something really affecting blizz much.

On a more theoretical level of desired optimization, HotO isn't a real choice. HotO loses to fathom for very obvious reasons (same +skill, no socket for facet, no +dmg, FCR isn't really needed, ...).

So you're really just looking at fathom vs. Doom.

On every single non-immune mob in the game, fathom is the guaranteed winner as every cold sorc even half-way built correctly will have those at the

Cap of -100 res no matter what. So all Doom gives you for dmg is 2 skills, compared to fathom's 3 skills, inherent cold dmg, socket for facet dmg and so on.

The only time Doom could ever win out is vs. immunes.

For that particular case, if you look at a fully geared blizz sorc, you'd end up with somewhere around -80 res and +95 dmg with fathom and -134 res and +60 dmg with Doom. Give or take, depending on exact gear choices (assuming no Infinity here cuz..yeah..no).

Factor in the starting 95 res post-sunder and say your base damage is X:
Fathom would give you X * 1.95 * 0.85 = 1.6575 X dmg vs. immunes.
Doom would give you X * 1.6 * 1.39 = 2.224 X dmg vs immunes (actually slightly less due to 1 less skill point for Blizz but let's ignore that for now).

Or in other terms, Doom has you doing about 34% more dmg against immunes than fathom. Go Doom! Sounds great!
On paper...

In reality, as noted above, more often than not, you don't need to optimize to that degree to annihilate all mobs on P8, including cold immunes. As a result, the gain from Doom is overflow/overkill more so than a real gain, more often than not, as going from "takes 2 hits" to "takes 1.49 hits" still means you're waiting for 2 ticks, just like "takes 1 hit" to "takes 0.74 hits" still means you're waiting for 1 tick. Looking at normal mobs and even most champs you encounter, that's the situation you often find yourself in..it literally makes 0 real difference. Every once in a while, you'll find an immune mob constellation where it does actually shave off a full tick in which case yes, Doom is better. But those are (at least in my experience) quite rare and even then typically don't matter as that extra tick would still happen in the same cast anyways based on their positioning/your aim. Same reasoning applies for "to Infinity or not to Infinity".

There is however one thing where you do notice a difference. Bosses. P8 bosses especially.
If you blizz down P8

Baal, you will finally have a target that actually takes a bit of time to kill. And there, you really will notice the difference in ticks to kill.
Thing is..he's not cold immune. Neither is any other boss in the game, outside of uber runs. So in any such scenario that you'd realistically encounter on a regular basis, fathom wins. By about 21%, give or take. 21% faster

Baal kills..you notice. Realistically 0% faster random CI mob kills..you don't.

Again, there will be the occasional, rare CI champ pack/SU where you would shave off a tick with Doom and where you may wish you had one because knowing the alternative, you will look at it and go "man, coulda saved that extra tick!" or in extreme cases even go "man, coulda saved another cast!". But at least in my opinion and experience, the impact of those is so low and the occurrences so rare that it will never outweigh the kill speed gain from fathom on something like

Baal.

Based on that same reasoning, albeit to a far lesser degree, I'd even take HotO over Doom if you can't afford a fathom as that'll at least give you another skill point to speed up

Baal with. But at that point, the difference will be quite minimal so it'd be a toss-up either way.

The only "real" argument for Doom imo is the

Holy Freeze as a defensive tool but if we're being honest, if you need that as a blizz sorc, that's simply a playstyle/practice issue more than anything.
Or running ubers..then yeah..def Doom.