From Nookipedia, the Animal Crossing wiki
The Snail (カタツムリ, Katatsumuri) is a small mollusk that can be found moving slowly across flowers or Hibiscus Bushes during rainy weather. When caught, it hides within its protective shell. If a player disturbs it, the snail retreats into its shell, falls, and disappears.
Donating to the museum
In Animal Crossing
"Let me make one thing perfectly clear:snails are not insects. Snails are members of the mollusk, wot! They are related to oysters, clams and more obviously to slugs. It's a well-known fact, you can't pick your relatives. Snails have soft bodies, which are protected by hard shells, and their eyes are on the tips of their tentacles. I've pondered from time to time, if one pulled a snail from its shell, would it than become a slug. Blech! The very thought of touching that slimy, mucous-covered body...Most foul! Utterly nauseating!"
In Wild World
"I should inform you, some cultures consider snails a delicacy... That means that someone, somewhere, would eat this. How I fear for that person."
In City Folk
"Ah, if you didn't know, here's a fact for you... Removing a snail's shell doesn't make it a slug! If you did try to pull off a snail's shell-- which I surely DO NOT condone-- its insides would spill out... I... Just got a mental picture of that. I fear I shall never eat again!"
Snails can be found on the upper terrace of the insect exhibit, on the flowers to the right hand side.
In New Leaf
Upon being donated, the Snail can be found in the room of the bug exhibit with the light in it, resting on a hibiscus bush near the light.
"Snails are mollusks that live on land and are related to shellfish like clams and oysters. One snail can play the role of both a male and a female, so it can lay eggs all by itself. Newly hatched snails already have a tiny shell, so right from birth they are easily identified. Most species have clockwise spirals on their shells, though spirals that go counterclockwise are possible."
Helix pomatia, also known as the edible snail or escargot (French for "snail"), is a species of snail that is sometimes farmed for eating. It is found throughout Europe, but was introduced to Britain by the Romans.
They appear on bushes when it is raining.