I thought, if they added a DH why wouldn't they add a DK too ?
Basically my idea about the class is to have a DK ( The Lich King as the hero ), with the hero ability being a 2 mana ability which can only target enemy minions and basically it would read " Give an enemy minion Deathrattle: Spawn a 2/1 Ghoul for your enemy ( Basically for you the DK ) " so after you kill that minion it would resurrect it to fight for your cause ( As DK's do, they resurrect slain enemies to fight by their side ).
Some strengths of the class would be board refill with ghouls ( Give the class some spells that give enemy minions the above mentioned Deathrattle ), some buffs for the ghouls and basically make it a Control based class, where you control the board with a swarm of ghouls and give them some Elite Death Knight units to lead your army of the dead.
Some of the mentioned Elite DK class units could be Kel'Thuzad in some way or another, Thoras Trollbane, Baron Riverdare and so on... Maybe some units from the expansion Knights of the Frozen Throne.
As for spells and secrets, would be cool to implement Runes, some frost spells and life drain into the class.
For the weak sides, I'm still not quite sure, perhaps make them weak-ish to big taunts and big minions in general, since having to smash all of your ghouls and minions into a big one isn't quite the best thing for you, plus they can only get a few ghouls of them that way. Perhaps also limit the card draw of the class.
This is just a basic idea of the class, needs a lot of refinment. I personally would love to see a DK class in HS, let me know what you think about a Death Knight class being added to HS and if you have any ideas for the class :)!