You have to go just a little bit south of the snail, where you can find a secret path to go further down by looking at one of those floor-eye things. The key is necessary to do this, and you'll see why.

3 years later... apparently the bit south of the snail was removed from the game (as of V. 1.3). Axe his belly and proceed.

I have just completed the snail section. It's rather simple. Open the door, look at the eye, and sneak thru the path that is opened by the eye. Eventually, you will find something to destroy. Break it, and the snail will leave the next day.

Felt the need to elaborate as these hints were not specfic enough for me when I was googling the answer and had like an hour before sundown. You need to keep a line of sight with the eye so that it stays open, walk through the shed door that you unlocked with the shed key, and about a meter in there's this hula hoop snake stump thing about the same size as the eye. That thing is supposed to open up and let you pass through if you are maintaining line of sight with the eye through the shed door. Hope this helps someone.

Thanks a bunch! I would never have figured that out by myself.

So i just stumbled on this part, as mentioned by #4 you need to stare at the eye for it to keep the path open.
- However there was a drawer in the way that i had to push to keep in contact, i have to admit i was a bit furious when it first didn’t work out while i keept my vision on the eye.