Building off of what VonC said:
Starting with Git 2.9, you can use this command to color words during add --patch:
git -c interactive.diffFilter="git diff --color-words" add -p
This sets the interactive.diffFilter variable for the call to add -p without affecting further calls. For me this is ideal because I usually want to run add -p normally, but sometimes want to run it with --color-words.
You can easily add an alias for this command like so:
git config --global alias.addcw '-c interactive.diffFilter="git diff --color-words" add -p'