What is stopping us from mixing 3D filament colors in an Extruder?
I just started with google and phrase "3d printing color mixing" and on the first place (in fact first two were valueless adverts) I got this Instructables - DIY Full Color Mixing 3D Printer.

How it works?

It uses magenta / cyan / yellow filaments and mixes it while printing with Diamond hotend.

It definitely does what you are asking for and it's exactly the same idea you come up with ;)

Overview


  
  Getting the controller board ready for three extruders... I hacked
  a RAMBo board to drive three extruders, however, you can use any board
  you want... (most people use a RUMBA due to it having all the
  pins/components needed for 3 extruders native on the board) 
  Rewriting Repetier firmware to get color mixing working on your
  machine.
  How to install, configure, and use the diamond hotend - tips /
  tricks / lessons learned / etc...
  My original Bowden extruder design and various ways to mount the
  three extruders for your set-up
  My universal magnetic effector plate and accompanying hotend mounts
  for quickly swapping various hotends. (delta specific)
  How to design multi-color models and making STLs that can be
  exported and used as a individual STLs or combining them into an AMF
  file for slicing...
  Configuring color mixing in Repetier and Slic3r to print above
  mentioned multi-color models.
  Anything else I can think of later that I can't think of now.
  Comprehensive overview of Quantum Mechanical Entanglement as it
  pertains to multi-color printing (just kidding, I don't understand
  that... But I will cover multi-color printing throughly)