At the beginning of the Hunt for the Horn, Moraine says Mat is needed to blow the horn. Is it a mistake? Was she given some information?

What do you mean "beginning of the Hunt for the Horn?"

Did you mean the novel, The Great Hunt?

 

Because she didn't say it in The Great Hunt, she said it in The Dragon Reborn, when she was with Perrin, Rand, and all the Sheinarians who saw Mat blow the horn... so yeah, I'm betting she was privy to what happened. Especially since the book begins a couple months after the events at Falme, so the reader should infer that some discussion and conversation occurred.