The hat room being the nightmare room is a decent theory but a couple things make me believe that it’s not the case. Firstly, Aurora and Henry both described themselves as being in a corner. The room inside the hate looked to be completely circular with no corners. Secondly, they both said they could see the other person through the flames, enough to see their eyes, The hat room is HUGE and unless they were sitting fairly close to each other they wouldn’t be able to see the other person’s eyes very easily.
One thing I haven’t seen brought up is what Regina tells Snow about what the sleeping curse does to a person. I found a good YouTube video of the scene (https://www.youtube.com/watch?v=f4DYyzJBmWg) and I’ll type it up here:
Regina: It won’t kill you. No, what it will do is far worse. Your body will be your tomb. And you’ll be in there with nothing but dreams formed of your own regrets.
What that means or if it even applies to the room in question remains to be seen. But I think this could provide some insight.