Eowyn's "disguise" - who was fooled by it?

[Lalaith]

Obviously Elfhelm knew. Eowyn was a highly skilled soldier (in the book at least, ahem) and must have got her training from somewhere. Maybe he was her mentor in arms and their understanding went back quite a way.

considering that in medieval times the bride didn't have too much of a choice

It's no good drawing direct parallels with real history and the Lord of the Rings as it does not take place in any historical mediaeval time.
Show me an instance where Tolkien has a woman of a free people forced to wed against her will. The only ones I can think of are Aerin, taken by the conquering Easterling Brodda, and Miriel of Numenor, who was taken by the tyrant ArPharazon. Both incidents take place under very dysfunctional circumstances.