Yes, this is possible. Just remember that you also add the mount in unit_prod11.txt file:
1. Copy a line with an existing horse, ie LiHorse, and paste it whereever you want.
2. You then rename the name from LiHorse to WhiteLiHorse and the BIF-name LIHORSE to CUSTOMX (or whatever your new BIF is called).
3. Make sure that the cavalry units refer correctly to your white horse and you're done

So much easier than adding new units since that would require icons and a whole lot more.

Good luck,
Duke John