Author Susanne Alleyn (who wrote Medieval Underpants and Other Blunders: A Writer's (& Editor's) Guide to Keeping Historical Fiction Free of Common Anachronisms, Errors, & Myths) said it best: "Do not borrow your period details and information from other people's historical novels & movies. Why? Because sometimes their author get stuff wrong. Okay, often they get stuff wrong. Especially in movies..."

People who blog about historical fashion often lament that Amadeus has one of the worst 18th century costumes. The worst part is it set bad precedents for future 18th century movies and TV shows. We have the impression that 18th century hair were all ridiculously big (often accompanied by how people never wash their hair and it must be filled with vermin etc). In reality that's simply not true. Even in the 1770's when the hair was at its biggest most women did not wear their hair that big all the time. The big hair and clothes you see in paintings are either court dresses to be worn in the palace in the presence of the monarch (most palaces have very high ceilings and massive doors) or their special occasion hair and best clothes. Just like how people today have some wildly impractical special occasional clothes but people don't wear ballgowns and tuxedos everyday.

So the movie took place in Vienna in the second half of the 18th century. In the 1760's hair was quite low. The biggest hair was found in 1770's and 1780's, for example here's Mozart's sister Nannerl, her hair adds 10 inches at the most and she wouldn't have any issues clearing doorways (again, they are posing for a portrait, it's likely that her everyday hair wouldn't look that big). Even Marie Antoinette wore more practical clothing when she's doing other things like horseriding. The very big hair was popular only very briefly and in the mid-1780's it became more of an afro.

Also note that the very tall feathers were usually on a hat and they were not really part of the hair.