Here's some of my input for some of the match-ups that I have experienced with my Snake.
ZZS - I think this match-up favors Snake, even if ZZS is running circles around Snake. Your attacks do as much as the sum of most of her combos. While, she beats Snake in the air, she can't beat Snake's jabs and tilts. The problem with ZSS is that some of her best moves that out-range and out-prioritize are often her kill moves (B-air and side-B). Her B is a poor match for Snake's grenades and Nikita missiles. Her tether recovery can be stopped by well aimed Nikitas and edgehogs; often forcing her to Down-B thus limiting her options. Overall, Snake can overpower him through strength and can camp her as well.
Olimar - An uphill battle for Snake, although the slope isn't that steep. Olimar would win the projectile war unless the stage is longer enough for Snake to grenade spam back, but cooking grenades takes time compared to his side-B. His range is dangerous, but Snake does alright once he gets into Olimar's face. His recovery is poor, so Snake can usually finish him off if Olimar must use B-up to grab the edge. I personally think it's pretty even with a slight higher percentage to win for Olimar. So maybe, a 55:45 or 60:40.
PT (Squirtle) - Snake can get through Squirtle's mobility and fast attacks through his raw strength. Squirtle also can't finish you off without Smashes early, while Snake can kill him with nearly everything. Snake can also camp him to a decent degree of success.
PT (Ivysaur) - A lot harder than Squirtle since Ivysaur has a spammable Razor Leaf as well as good range. Ivysaur can also kill Snake with well placed non-staled U-airs and U-smashes. However, Snake can still beat him with his tilts (well, he beats a lot of people with his tilts). Also, Ivysaur has a really bad recovery since he must grab the edge and dies to edgehogs a lot. Still favors Snake.
PT (Charizard) - Imo, the only Pokemon out of the three that can match Snake evenly. Charizard has really good range in his tilts and is heavy. His aerials will usually beat Snake in a direct battle. Also, Rock Smash is really good against Snake, especially short hopped. His ground speed and grabs are useful against Snake as well. His D-throw (Makeout throw) does a nice number and knocks Snake pretty far back. Edgeguarding Snake is very hard if Snake is knocked up high. Charizard also should use his B-up since Nikitas will hit a gliding Charizard. This match-up is kinda even, and really depends on the stage as a factor.
Sonic - I think Snake has an upper hand, although if the Sonic is a smart hit-and-runner, it becomes a game of endurance. This of course favors Snake, who will outlast Sonic's hit and running tactics. Sonic also must approach Snake or get projectiled, which of course gives Snake an advantage. Sonic also can't disable mines without using his shield. I think edgeguarding is about even for both sides. Snake should win through outlasting and be able to kill Sonic early through direct KOs since Sonic needs to limit using his good moves for... KOs.
Pit - While a Pit can camp the crap out of Snake, Snake can approach with powershields (Pit's arrows are pretty easy to powershield since they're shiny and have a steady speed to it). Pit can't really compete with Snake on the ground, since Snake will simply overpower him. Pit will usually do decent against Snake, unless Snake is using reverse B-airs. Snake also has the advantage in edgeguarding, since Pit's B-up can be gimped a lot with Nikitas. Finally, Pit can't kill Snake as early since Snake not only lasts longer, but also has way more options. It's about even, since Snake will win once he's close and gets to use his groundgame. However, Pit can run away or try to force an aerial battle. Smaller stages for Snake, and bigger stages for Pit.
Overall, Snake does quite well if he can outlast and get kills early. If he can projectile camp, then that's even better.