The textures of the vanilla reindeer in Skyrim seem to consist of three files: "reindeerbody.dds", "reindeerbody_n.dds" and "reindeer_sk.dds". I know what the normalmap one is, but the other two are very strange. The body dds is almost invisible so I have no idea how to edit it. And the sk_dds is extremely small.

Could someone explain to me how I should proceed, if I just want to make minor color changes to the skin of the reindeer?

The reindeerbody.dds is the main texture for them and where you'd want to do your retexturing. Not sure what you mean by it being almost invisible, looks perfectly fine to me?

You wouldn't need to change the _sk.dds, that's a "skin" texture and best if left as is. The normal map you'd only need to change if you make edits to the texture that affect the original fur layout (besides colour).

It looks "almost invisible" to me. Look here: http://postimg.org/image/c56zeaehd/

Hm, Gimp, in a different language even. That is definitely not right.

Sorry, I can't help you any further (I'm a PS user), but my guess would be you have some setting on that's making it transparent or there was something in the Open dialogue box that caused this.