Do Balrogs Have Wings?

[Hookbill the Goomba]

Although, Morsul, one has to ask (perhaps for another topic) were Dragons captains over Balrogs or vice versa?

they have wings because Balrogs are actually dragons!

But even then, not all dragons have wings.

The whole Balrogian Wings debate is hard to resolve. In reading this topic, I personally have changed my opinion thrice, from no wings, to wings, and back to no wings again. It would be interesting if someone found a letter by the professor telling us a) how may wings Balrogs have and B) who Bombadill is, thus stopping all this silliness.