This mod will change your horse to the texture name you prefer! You can also enable a saddle overlay and choose the color for it. There are variety of horse skins to choose from that are available in this mod along with the optional saddles.

To install it, it requires you to install the latest SMAPI, and Content Patcher. 
Extract into your \Stardew Valley\Mods\ folder..
Then, you can run the game through SMAPI to generate a config.json file.
Next, you will need to open the config.json file with a program like Notepad.
And run the game using SMAPI!

To uninstall, what you need to do is to delete the folder you put in your Mods directory.