Don't use the 128x128, that's way too small of a resolution. The UV image is scaled to 1024x1024, so you could create a new texture with that size and then use the UVs, or scale them down to a standard 512x512 and work with that. I didn't create a new texture, since I don't know what exactly you want the hat to look like, so I'll let you make your own. You can make it as big, or as small as you want.
Either way, you'll be overriding the old texture, so it's best to back that one up.
I suggest backing up the AppleJackHat.mesh file as well, in case you ever want the old one back again. After that, just replace the one in your FeralHeart\media\items with the one I made. Ignore the .MESH.XML file.