The reason that I did applied color instead of just mixing the color is that the terracotta has tones to it, and I didn't want a flat color for them.
To color buttercream, you need to keep a couple of things in mind. First, use thin coats of color and keep them light. It's better to do a few thin coats and wait in between than it is to try to get a dark color all at once.
The buttercream will resist the color if it's too heavy, and it can pool up and drip, so use a light hand. Fondant will absorb the color better, so you can be more aggressive about it if you're using fondant.
For these, I started with a coat of orange, then a coat of red, then ended with a coat of brown. By applying some sections more heavily than others, I got the variation in tones that I wanted.
When you're done spraying buttercream, keep in mind that you should refrigerate the cake because the color is just on the surface of the icing and will rub off easily if you touch it when it's soft. Once the buttercream hardens up in the cold it will hold up better if someone happens to knock into it.