I don't really understand what people mean by this sound. It seems like most of the time people refer to it, as a bad thing, yet to me "brassy" is a good thing. I found an article that talks about the "sizzling sound", which they use synonymously with the "brassy" sound. I always thought the trumpet sizzled more as it got louder, and I'm glad to find an article confirming that, and that my ears aren't messed up or something! (well, maybe they still are messed up in some ways....I forgot I have an ear wax problem....haha) It also explains why the really-loud Lee Morgan had an incredibly resonating, sizzling sound (IMO, at least) compared to other solo trumpeters. It's an article from the ITG.
Also, it's normal to hear the "sizzling" of the trumpet sound from the player's side of the horn, right?
Now, back to the "brassy" again... is there a "bad" type of brassy?
(Of course, if you sound "brassy" when playing SOFT, that probably means something is wrong....)