How can I change the way the GHC compiler displays error messages?

Do you want to change GHC? well, it's open source, so you can change it however you want and recompile, but that would probably be a giant overkill.

If I really wanted to, I would make a program that calls GHC with the arguments it receives, reads the output, processes it, and then prints.

You can do this with System.Process

. readProcessWithExitCode

, in particular.
You might be tempted to use the readProcess

simpler API for it, but it will only read from stdout

, and you almost certainly want it stderr

too.
Plus the exit code in the previous function can also be very helpful: you could know if the compilation succeeded or not, even without parsing, but just by looking if there is an exit code = 0.