If I had to guess.. when I'm stone cold sober and I go into a conversation, I'm somewhat consciously aware and focused on having to breath properly in order to speak fluently. And that's when the nerves kick in that I'm going to mess up and improper breathing kicks in and wrecks the sentence. When hungover, most of your consciousness is focusing on whatever pains your body associates with a hangover. All you're worried about is getting that next sip of water, breakfast (maybe) and trying to function properly. Speech and breathing properly is the last thing to cross your mind. Thus you do both normally as anyone else would.