I recently bought my dad Forza 4 for christmas and he's now telling me that you need to have a gold membership on xbox to even customize your cars at all. Now, my dad's not very familiar with video games at all and I think he was confusing this with an ad to buy DLC BUT, just in case, DO you need xbox gold to be able to do this? and if not then how? so I can explain it to him.
You do not need a gold membership to customize or tune cars, however, you do need it to upload created paint jobs, tuning files, and vinyls to the storefront to sell to other players, to join a club, or to share things with a club you have joined.
If you want to create custom vinyls for your car, you can go to Play Career > Paint > Create Vinyl Group. Once you are in the menu here, simply create your design layer-by-layer and, once you have what you want, save it. (Doing this the first time also nets you an achievement.)
If you want to tune your car to your liking, ho to Play Career > Upgrade > Tune Setup and you will be presented with the option of changing the setup (tuning) of your car. When you have things how you like, hit the Start Button and select Save Current Setup to save the Tuning File.