I've been experiencing this issue on and off since starting to play Hearthstone. I'll get intermittent periods where an action, like casting a spell or making an attack, will take several seconds (up to 10-15) to register. While this is occurring I can't do anything. Most of the time it's just an irritation but the delays are big enough to mean that I can end up failing to complete a turn and have lost matches a number of times this way.
Just wondering if it's an NZ thing, maybe an ISP thing (I'm on bigpipe, so maybe the NAT causes issues?) or something in my home network. I've had the problem on US, Asia and European servers.