I played Ginger (5th on MI Melee PR) in Snake vs. Samus last night, and we went about even overall. Now I promise this is related, because I started to really develop an idea of Snake's neutral in its most challenged form. Ginger plays a really defensive Samus (it's not his main, but it's probably 2nd or 3rd in the state at this point) with a lot of projectiles, UpB OoS and the like. So I can't really let him be far away, but I can't get too close to him either. What I could do, though, was use mines and C4 and grenades to control where he could be. When we play on PS2, I simply planted mines and C4s on the platforms so that he couldn't missile cancel on them without getting punished for it. This forces a different sort of playstyle from him where he'd try to space out tilts and the like. I'd duck under f-tilts trying to bait out down tilts or up tilts so that I could dashdance grab these and get a grab combo, usually up throw to C4 or up air or nair. Samus is super floaty so I don't need a whole lot of percent. Once he gets to the point where he doesn't try to use unsafe tilts (or realizes that downward angle f-tilt still hits Snake's crouch), I would start grenading his tilts so that he'd take on damage in that way as well. Then he has the option of either baiting my own unsafe options or being aggressive in some other sense (i.e. being close to me) where the whole cycle repeats again. Another thing he tried to do but I punished really well was to ledge camp and attempt to bait me into something, where I just planted a mine to limit his movement and then turned it into an edgeguard. This specifically lets me get a grab near the ledge, meaning I can down throw techchase Samus and cover every option just by crouching (since getup attack is too high to hit Snake's crouch).
This is how I see that Snake's tools can be used in the Neutral most effectively: you don't approach. Instead, you eliminate as many of their options as you can until the only one left is for them to approach. Samus does this exact same thing, but I think Snake is actually better at it overall due to the lack of movement investment needed to establish and maintain your stage control (mines just need to be placed once and can be moved at any time vs. missiles disappearing rapidly by comparison). This basic concept remains the same for almost the entire cast—Snake's punish game is his strongest asset whereas his approach is likely his weakest. There's no point, therefore, in trying to approach when you can just let your opponent do it, read it, and then react to it with the proper punishment. That's what DACUS is. That's what dashdance grab is. That's what dash cancel tilts are. Grenades are a way of controlling the stage. Mines are a way of controlling the stage. C4 is a way of controlling the stage. They all also happen to be threats of combos, which is why they work to control your opponent so well. Some characters are compelled to approach, like Falcon and Fox, but they never need to approach and actually perform better when they don't.
The idea here is to maximize your punishments so that you minimize the amount of times that you have to win the Neutral, because winning the Neutral means that you successfully read your opponent: you had to make a guess, and that guess had to be correct. It's the same whether you approach or not. The trick is really to just become familiar with a given character's options as well as the player's tendency to favor some options over others. At the same time, you need to understand those options and the space they cover so that you can position yourself outside that space, while also understanding your own options enough to know the balance between safety and opportunity.