Can you update a brass ceiling fan cheaply?

If you want to take them down to work on them, I think some Rustoleum in a less shiny metal finish would look good covering the brass. If that isn't an option, and you have to leave it in place, you could do someting like a white-ish glaze to dull down the brass.

Paint

https://www.hometalk.com/search/posts?filter=paint%20ceiling%20fan

If you can, spray paint the parts in a new finish such as oil rubbed bronze or aged gold. Be sure to clean and apply deglosser to prep and get a durable finish.

You can spray paint both the motor cover and the fan blades as you wish! The motor cover will be more difficult but can be done. Your best bet for that is to use Rustoleum for metal. Buy a small can so you can brush around the air openings of the cover.

Painting the fan blades is super simple! Merely unscrew the holders from the blades and take them down. Spray with Rustoleum, paying attention to the sides of the blades as well.

Rustoleum has some fantastic new colors and finishes including things such as a gorgeous baby blue in a matte chalk finish. You can easily pick colors that go with your decor and update the fan at a low cost.

Thank you all for the advice. I will paint it. If I paint them with the oiled bronze what color should the blades be?

FYI Gold toned metal is coming back in style.