When pictures or animations are set at design-time, you do not need to distribute the pictures or animations with your application. This is because they will be included in your program at compile-time. Redistribution of images is only necessary when the images on the button will be changing at run-time.
In order to keep the final EXE program size smaller, avoid using bitmaps larger than the dimensions of the button: if the texture is smaller than the button dimension, it will be tiled in order to cover the whole button surface.
The texture application does not take account of the current button colors: if you want to mix the texture with another color take a look to the Texture.ColorToMix property.