The last time I ate there, MK closed at 9:00 and CHH closed at 8:00. I would guess maybe around 10:00, but that is just a guess. You can get a times guide the day you're at MK with the actual closing time.
You'll really have to check the times guide when you get there. I don't think there's a fixed closing time.
Last time we tried to eat there, around 6:30pm they had closed at 6! There were a LOT of people trying the door so it's not like there wasn't a demand. And I think the park was open until 10pm that night too.
The CHH closing time remains a mystery to me. I've been there on days when MK was open til 9pm & it closed at 4 or 5pm....and I've never seen it open during EMH. It's my favorite CS in MK and am always disappointed when I can't get there until after it's closed!