Ouch, Falcon VS Snake isn't that great. But wait, Snake VS anyone isn't that great! Silly me.
Now then, I'll give you some solid tips. I haven't played many falcons, but find some Snake players using the friend finder and experiment with moves that can stop mortar slides midway through. I know that Ness's yo-yo can do this (as it has a disjointed hitbox), but I don't know about any of Falcon's moves. Try an F-Tilt, I have a feeling that it may work. If you know any moves that Falcon has that have disjointed hitboxes, try those too.
Secondly, watch out for those grenades. Throwing them back IS a good option, but be careful, most Snakes know about grenade stripping, which makes you automatically drop your grenade. Yes, Snake is psychic.
Every Snake, whether he or she likes it or not, loves to spam F-Tilts. Now, the F-Tilt is a great move, but it has some ending lag. Use that to your advantage.
Snake's air game isn't too bad. Be warned, most of his aeriels have high priority. I suggest experimenting quite a bit. I know that I don't like U-airs from ANY character. Just watch out for Snake's dair or nair, so try to hit with just the edge of your foot when you U-air.
Snake's Achilles heel is hands down his recovery. Sure, the Cypher is a great move and all, but it can still be defeated. First of all, any move that does more than 7% damage with a single hitbox (no multi hit moves, so that means Falcon's nair) will knock Snake off the Cypher. This means that most dairs will do this. I've been spiked a LOT while on the Cypher. (But I've learned to not get spiked as much now
)
The WORST thing that can happen to a Snake player is to be gimped. This isn't a hard task, I'm sure you can do it.
Hopefully, I provided you with some help.