camping is one of pits best strats here, use your arrows any and every time you get a chance, as it will force snake to approach you, trying to approach him is almost always a death wish, make him come to you.
your arrows , like someone else said, are great for screwing up his nade game, and snake gets very screwed over without his nades, though just remember, be prepared when he gets close, as his tilts still have a WTF Retardedly broken range, speed, and power.
when snake is near you, try to get him in the air, he ***** pit bad up close on the ground, but his aerial game is a joke, and get him offf the ledge and you can go for some pretty good kills.
also, one thing EVERY player needs to know about snake, regardless of whether its pit, or not, when snake is using his Up B, if he's close enough for you to grab him near the edge, GO FOR IT, but DON'T PUMMEL him, OR throw him at all, wait for him to break away from your grab, its a tiny glitch that works on both snake and sonic if i remember, they can't use the up b again unless you actually did some damage to em or they touch the ground, since you are holding em over the ledge, where they aren't actually touching ground, and you haven't did any damage to em, the game still considers them in free fall mode, so unless he can bring out a c4 in time and bomb himself back up, he's pretty much dead. only characters this can't work with are ones that have tether grabs like link and samus that i know of.
oh...and btw, did i mention you should camp with your arrows?
no joke on this folks, forget the arrow loops/fancy trix, go all out camping with normal arrows on him, this is coming from someone who has alot of experiance fighting snake. back when i tried to convince myself that arrow looping was acutally useful.....each and every snake i'd face slaughtered me, second i stopped with the arrrow looping gimmick, and started camping my *** off on em with arrows, suddenly my most hated match became one of my favorites, i don't have nearly as much trouble with snake anymore, i know there are some pits who still refuse to believe that pit NEEDS to camp with arrows like mad in certain matchups, but honestly people, he does, watch the japanese pit mains, they camp like mad, and they tend to do a HELL of alot better with pit in tourny placings then we do, get out of the mindset of "pit doesn't need to camp to win, SEEE!" because folks...he honestly does, I've never met a falco main that didn't camp there *** off, why? because they realise he has an amazing projectile, pit mains need to realise this about his arrows, quit with the arrow loop gimmicks people