Do Balrogs have... Horns?

[Hookbill the Goomba]

While trying to convince my brother to draw a picture of a balrog, I looked up some previous artwork in which they are seen. I also read him the descriptions as found in The Fellowship of the Ring and HoME VII. When we looked at this I pointed out, in my attempts to convince him of the none wingedness;
"See, no mention of wings in HoME." To which he replied,
"No mention of horns either, but they always seem to have those..."

This got me thinking. There always seems to be certain traits that the Balrogs have; Horns, tail and claws but none of these are ever mentioned in the books. This, of course, is not confined to Balrogs, but I'm sure other characters and creatures have inadvertently gained characteristics for no reason. We all remember the 'Do Elves have pointed ears' debate.

So my question is this...

Why is it, do you think, that so many things seem to gain things in our imaginations? I never really thought about a Balrog lacking in horns until now and it seems to make sense. Is the artwork always so influential? Is it the fact that the Balrog is thought of as 'Daemonic' that the horns and all that come about? Why does the Balrog's 'hair' or 'mane' always get less attention, even though it is one of the things Tolkien actually mentions. Do we always take liberties in our mental pictures of characters and creatures?

In opposition to this, I must present Morgoth. There is a lot of artwork about him with vastly differing ideas. This probably has a lot to do with the fact that he is never (or, at least, doesnt get much) described physically. there are pictures of him with a pig-like head, with a Movie Sauron look, with monkey face and (as Ted Narusmith portrayed him) with grey arms and black finger nails.

What think you people?