Do Balrogs have... Horns?

[obloquy]

Why is it, do you think, that so many things seem to gain things in our imaginations?

Because we've all seen either John Howe's drawings, or at least part of Bakshi's animated movie. Tolkien's words alone do not conjure images of horns, unless demons are already associated with gargoyles or bat-men in your mind. Biblical demons are not hideous monsters, they are angels who made bad decisions; similarly, embodied Umaiar do not conform to some medieval demonic archetype.

They are probably physically daunting, but man-shaped, and assuming they are truly incarnate, they are also probably afflicted with the same inability to conceal their inner evil that came with incarnation for Sauron and Melkor.