Being a Snake player, I've versed a number of other Snake players but they all seem to make one mistake, that is being grabbed while recovering. The Cypher hits the grabber therefore cancelling the grab and making snake fall to his death, every person I've done this to seem to have never of predicted it and just fall. Its never happened to me, though living in Australia, i don't come around a good player in basic brawl often, so what i wanna know is that; Is it possible to actually recover from being grabbed like that? (say the stage is Final Destination or Luigi's Mansion)

Drop a C4 and blow up Snake. He will get his upB back too.
Or better yet, upB near the ledge but outside grab distance and airdodge towards the stage to land. This usually works vs people expecting the grab release trick to get Snake.

PS
If they pummel or throw Snake he can UpB; it must be a grab release which can be forced by his recovery thingy hitting or will happen in time.

Few Snake players who aren't bad will make that mistake on a routine basis. Most Snakes will stay away from recovering low and will go high instead.

Occasionally some will recover low, in which case they can do what Rizen just said. Thr way to avoid being instantly released from a cypher grab is to let Snake go straight up and not straight up. When he's grabbed the cypher will follow whatever trajectory he was going. If it goes straight up, it can't hit the grabber.

You can also do this grab release trick on Sonic and Mr. G and W, though it's not as easy. It works because Brawl doesnt give you hitstun for simply being grabbed, and you don't get your up special back unless you go into hitstun.