With a mixer, beat together the cream cheese and butter until smooth. Add vanilla and brown sugar. Slowly add in powdered sugar until mixture is combined.
Evenly divide the mixture into 3 separate bowls. Set one bowl aside (for the white) and then add the red color to one, and the blue color to the other. Start out with just a couple drops of the food coloring and add more until you get the desired color.
Cover a plate with wax paper. Take the red mixture and form into a small cheese ball on the plate. Freeze for a couple hours to harden. :Place the remaining 2 bowls into the refrigerator to use later.
Remove the cheese ball from the freezer and evenly cover with the blue mixture (just like how you would ice a cake). Place back into the freezer for another couple of hours. Remove, and cover with the remaining white mixture. Return to the freezer to harden. Finally, cover with sprinkles and place into the freezer until about 20 minutes before you're ready to serve.
Serve with graham crackers, fruit, or cookies.
Notes
If you prefer something easier, you can serve this as a dip instead of a cheese ball. Simply layer each color into a clear bowl (be careful not to mix the colors together) and cover the top with the sprinkles.