There’s already a function for applying color to comint buffers. You simply need to enable it on compilation buffers:
(require 'ansi-color)
(defun colorize-compilation-buffer ()
(toggle-read-only)
(ansi-color-apply-on-region compilation-filter-start (point))
(toggle-read-only))
(add-hook 'compilation-filter-hook 'colorize-compilation-buffer)
Color writing programs should check the TERM environment variable and the terminfo database to check if the terminal supports color. In practice, a lot of programs ignore this and rely on a user setting. Emacs will set the compilation terminal type to dumb by default but this can be overriden by setting the compilation-environment variable.
Update: Note that in Emacs 24.5 the two calls to (toggle-read-only) in the code above are not needed.