Will it be cold in the ice arena?

I know this must sound like a dumb question. How can it not be cold when you’re sitting in the same room with an immense ice cube? But I haven’t attended an ice skating event since I was a little girl, and now I’m going to see the Olympic skaters. I don’t know if it will be cold enough in the stands to warrant a coat because the room is cold, or if when you’re away from the ice itself and in a crowd you can just dress normally for indoors.

So do I dress as if for a cool indoor space, a warm indoor space, or a cold outdoor space?