This is really an issue with the films. The book doesn't have the (admittedly cool) scene of the Witch-King defeating Gandalf. In the book, Théoden is ready to face TWK, but his horse panics, falls and crushes him. Then no one else has the courage to stand against TWK, except Éowyn and Merry.

The Witch-King in the books is not a seven-foot dude wielding an impractical (but cool) weapon with a spiky thing on a chain bigger than Éowyn's head. He's not that physically powerful. But he doesn't need to be, because he can *frighten* anyone but the very bravest.