The 'brownness' of your frosting will depend on whether you use cocoa or melted chocolate, and how much you use. Generally, cocoa will give a darker color to most frostings, while melted chocolate will be a lighter brown.
Here's a link which basically describes the difference - http://www.baking911.com/cakes/butterpound.htm
- this is a great resource for baking in general!
And to make it even more confusing, my hubbie's family (from NC), calls a yellow cake with chocolate frosting a 'chocolate' cake; a chocolate cake w/chocolate frosting is always called 'devil's food'!