This fight is...clunky. It requires finesse and coordination, but until you reach it in heroic mode (which I have not, and few have), it can be brute-forced through with only a few adjustment wipes.
The biggest, most essential part of this boss is the distribution of Permafrost. As a healer, this is obviously not your concern unless the boss burrows. My guild DPS'd the orbs until they were low, then attempted to Death Grip them into position. Though possibly the best plan, it is still rather unwieldy as the orbs start floating away and up as soon as they are released, making early Death Grips ruin positioning.
Why is it important to position Permafrost? To prevent burrowing. The adds are able to burrow, but not if their hitboxes are completely covered by the Permafrost. And by completely, I mean absolutely no portion of their hitbox can be uncovered or they will burrow. With the adds, this means that they burrow, then repop after more adds spawn, quickly overwhelming your off-tank.
Very important for healers (and everyone else) to know: never stand in front of the boss! He cleaves, and it hurts. The tank has priority on movement. You make way for him, not the other way around. Another thing to watch out for, as well, is that the main tank will periodically get frozen, basically stunning him and locking him in place. Keeping HoTs stacked and controlled cooldown application (with conservation for the last 30% in mind) will allow your tank to survive. As well, watch for any raid members with the Penetrating Cold debuff, as it will knock off a 2k+ of their HP each 3 seconds.
When Anub'arak submerges, the whole raid needs to clump together on Permafrost. This will prevent a large amount of damage coming from the submerged Anub'arak (his hardest hitting attack cannot penetrate Permafrost) and allow for controlled AoE of the scarab adds. Watch for the large ice spikes that form up around your group; as soon as they pop, move to the next patch of Permafrost. They do no damage, they simply signify that Anub'arak has broken that patch of ice and it will despawn, leaving you defenseless. He will "pursue" raid members, but so long as everyone is clumped up in the middle of a patch of Permafrost and not on the edges, he remains ineffective. After the fourth submerge, he enrages and it's a wipe.
At 30% life, Anub'arak will cease burrowing and cast Leeching Swarm. This is where it becomes tricky, if somewhat boring, for healers. I had to all but stop healing except for occasional HoTs on the tank.
What? But why? Shouldn't the last 30% be harder?
It is, it is. But it is harder because it requires a large amount of control, and HoTs are somewhat of a loose cannon. You see, Leeching Swarm takes 10% of remaining life (not total) from the person it is applied to, and it is applied to the entire raid, to a minimum of 250 health. That means the lower people are, the less they heal the boss for. You want to juggle your raid at about 50% life to avoid deaths from Penetrating Cold, with only your tanks at max life. Since adds stop spawning at this phase as well, all remaining adds should be burned down to spare your OT's life requiring max fill. If you have multiple Restoration Druids, one or two max should use HoTs to counteract the swarm. Otherwise, all straight healing spells should be used, and you should be ready to cancel those heals at a moment's notice by jumping, hitting a cancel macro, esc or moving. I quite literally did almost no healing due to our raid having seven healers for the fight and other Druids covering the HoT portion. This is a little frustrating, but as Heroic mode will be draining 20% of remaining life, I have a feeling things will be a bit more active.
Well, that's the fight! Good luck, and my the loot gods smile upon you. Also, watch out for Death Knights who pop Path of Frost too early or Shamans who just have a sadistic desire to watch you break your bones on what should be a forgiving pool of water.