I will do my best to give you some details, not being a native English myself, too
the horse01_sk.dds, is a subsurface map. _sk.dds textures mimic specific kind of materials, most often slightly translucent ones, and/or those that disperse light and not just reflect it (specular), in not so usual ways. Materials that light partially penetrate, and is scattered by them, like Candle wax, Jade amulet, or human Skin. Hypothetically, it kinda makes sense for a horse skin too, but Skyrim engine is so barely efficient at this that it's rarely worth it. And it's handled far worse in Skyrim SSE, by the way, with different kind of issues (the infamous 'Bronze shine', on characters, at least if I remember correctly).
" I tried the nif with and without this file and there was no difference."
While this _sk map controls how and where on the model the _Soft Lighting_ effect (Bethesda's odd name for this), will be applied, to effectively remove the lighting effect you need to remove/uncheck the 'soft lighting' SLSF2 flag in the material node. Here's how to easily do it in Nifskope, just in case you didn't already know, or other modders would like to:
"What do you mean with save in dds1 RGB ? DXT1 without alpha? But I need an alpha channel because the mane and tail have transparency and this must be DXT5 - as far as I know."
Sorry for the imprecision in my last post, I meant for this _sk.dds file only, when I said that ;). these _sk maps don't need an alpha. Currently, horse01_sk.dds is wrongly saved in DXT1 ARGB (1 bit alpha: unusable for most other purpose even), while it should just be saved in DXT1 RGB (no alpha at all). It's not a gamebreaking point though, don't worry. Just unnecessary data.
now, don't worry: The transparency of the mane and tails are not handled by this texture, but by the alpha channel (yes!), of your diffuse texture: hosemaintailWhite.dds (which is in the correct DXT 5 format ). So you can safely remove the soft lighting stuff for the horse body without affecting transparency.
To be a bit more precise and technical, the transparency is also handled by other factors in your nif file, not just the diffuse alpha: the node 'shader flags1 'Vertex_Alpha' of the node 20 BSlightingShaderProperty for the tail & mane mesh, its child node, 22 NiAlphaProperty, and the vertex alphas of the NitrishapeDATA (node 16) - labeled in Nifskope as 'Color 4 subdetails for each vertex colors in the nitrishapedata. Sounds complicated, right? All these factors are working in conjunction to fine tune the transparency effects of your horse mane and tails, but since such combination of transparency factors is not always required, nor even always present for all kind of meshes (some don't use the vertex alpha tricks, some only use that but without niAlphaProperty nor texture transparency...) I get that it might sound more complex and possibly confusing at first than a lot of modders would think (even experienced ones).
if you have other questions, don't hesitate, Tasheni. Here or on Nexus by pm, if you'd like (I have the same profile name out there: Ambershore), since DC forums will close sometimes soon, sadly.