As someone who mains both WAR and DRK, I do not recommend using holmgang or living dead at all if you can help it (IN DUNGEONS). I have two reasons, the first of which is I believe that DRK and WAR both have enough cooldowns to not need to resort to using their "ultimates." The second reason is that using them freaks healers out.

Holmgang, for example, has to be used at the last second to REALLY wring use out of it, and if you're needing to use it, it's because your healer just can't deal with the shit going on, for one reason or another. At that point there is little your healer can do. A lot of that applies to Living Dead as well.

Hallowed Ground, on the other hand, can and should be used as often as possible in dungeons because of its design. Some dungeons have layouts where there exist two particularly huge pulls, at the start of the dungeon, and nearing the end of the dungeon. That is the perfect opportunity to use hallowed ground in both! HG is best used as the very first cooldown, to be used right when they're on piling on you and before your HP plunges. I like to chain sentinel as my second cooldown, queuing it as soon as HG falls off in order to afford me a grand total of 20 seconds with extreme durability.