That’s a great idea, but we don’t have any documentation specifically geared toward guiding you through this. If you are purely changing the styling, perhaps you could do this simply by leveraging appropriate CSS classes applied to the body (which will normally include a front-page specific class when you are on the front page)?
If you want to go beyond that and build and use separate templates according to some criteria (like whether or not it is being pulled in to the front page) you could certainly do so, but that’s a little beyond what we can help you with here.