Yes, my first team finally 80! :-)

[Zub]

Does this mean ordinary heroic dungeons are in fact easier than normal icecrown?
So I should play some heroics before even trying the normal icecrown dungeon?

I would say the icc normal dungeons are indeed harder than older heroics. particularly Halls of Reflections.

You should be able to do Garfrost / Ick in Pit of Saron and James Brown in Forge of Souls, but Tyrannus/Devourer might be rough, and Halls very hard.
Then again, it drops better loot, and emblems.