It depends on what time period and type of medieval music you are referring to. We have many specimens of musical instruments that we can reconstruct and get a sense for how they sound. But if it's before ca. 900 AD (or later if we're talking about secular music), we probably don't have a written record of the piece in question. And even if we do, there's very little to tell us about how anything that wasn't just an a capella choir performed their music. So it's hard to know how these instruments were put together. All of this is explained in greater detail in this post, with insightful comments by /u/erus and /u/azdac

But part of your question is the popular view of medieval music as propagated by Hollywood. That's a question that I'm not sure I've seen answered on here before, and is a rather interesting one! I admit, though, that your description of "airy flutes and brassy horns" does not ring a bell for any imitation of medieval music that I've heard. Perhaps you have specific examples in mind?

Given the posts above, you would be right to imagine that reconstructing the sound of medieval music involves a lot of guesswork. But the historical performing community has come to some general consensus about what may have been stylistic at the time (again there are examples in the post above). What this community does may and sometimes is taken as an "authentic" sound that is then imitated in Hollywood. This is about as good as one can expect things to get given out knowledge limitations. But other times, there will be a significant spillover from the sound of other Hollywood tropes. This includes things like the Fantasy soundtrack alla LOTR or GoT. It also includes generic battle sequences, etc. These are sound worlds that have their own origins, and they may mix with various elements of "authentic" medieval music to create something that's appropriate for the film/show. But it's hard to get any more specific without looking at the specific kinds of examples that you have in mind!