Due to its unusual body chemistry, A barrow wight has no need to breathe. It is humanoid.

When he came to himself again, for a moment he could recall nothing except a sense of dread. Then suddenly he knew that he was imprisoned, caught hopelessly; he was in a barrow. A Barrow-wight had taken him, and he was probably already under the dreadful spells of the Barrow-wights about which whispered tales spoke. He dared not move, but lay as he found himself: flat on his back upon a cold stone with his hands on his breast.
The Fellowship of the Ring, by J.R.R. Tolkien