You could do that, and I understand why that would seem like the simplest option given your lack of interest in other mods.
Overwriting game files directly has a lot of drawbacks though, and SMAPI comes with some built-in positives like console commands that can help you when you are stuck, automatic save backups, and a detailed log you can use when you need help. You don't need to install mods you're not interested in, but the process will be much simpler if you decide to later, and you'll have a lot of help available from the general modding community.
I suggest this route:
- Install SMAPI. (Instructions for Mac and Linux if applicable.)
- Download Content Patcher and extract it into the Mods folder SMAPI created. (See this page for examples of installing mods if needed!)
- Download the attached mod and extract it into the Mods folder as well.
- Edit the sprites in its assets folder, using any image editor that supports PNGs. (paint.net, GIMP, pixel art software etc)
- Launch the game and see if your changes took effect.
For any future modding of game assets, you'll definitely want to start with
unpacking the game files. (The horse would have been in the
Animals folder, as are all the dog and cat variants.)
If you should want to make your own packs for Content Patcher in the future, it's
extensively documented and lets you make changes to the game's assets under any combination of a staggering assortment of conditions. For example, if I wanted to have tons of variants for my horse (say, for every season or festival, or even my choice of spouse), I could add all the pngs with certain names to the assets folder and just edit one line in the provided pack's content.json to make SMAPI use them all at the appropriate time.
For now, on Nexus and ModDrop there are other templates for other assets you can use if you want to branch out :)
(Making packs for CP is pretty simple once you get the hang of it, and doesn't require any programming! It can still be kind of overwhelming at the start when you're just trying to get your horse in the game, which is why I included a pack that does nothing except replace the horse and its menu icon. You're welcome to use it even if you want to release it as your own pack; you'd just need to edit the manifest.json in any text editor to change the author details to your own. Feel free to ask for help if you decide to take the leap! )