where it is and what it looks like
The Snow biome, which the Angler insists on calling the Tundra, covers a stretch of surface in snow and ice with boreal trees on top and permanent falling snow that is purely decorative. It always generates on the same side as the Dungeon, opposite the Jungle and the Underground Desert, and it runs downward, becoming the Ice biome once you reach the Cavern layer. When it rains anywhere in the world, the snow gets a blizzard instead, and visibility drops hard while it lasts.
how dangerous it actually is early
It is a step above a forest and nothing worse. Ice Slimes and Frozen Zombies hit a little harder than their ordinary counterparts and the ground is slippery, but basic armor covers it. The thing that catches people out is water. On Expert and Master, touching water or shimmer inside a snow biome applies Chilled, and it stays on for five seconds after you climb out. Getting slowed for five seconds is a problem at exactly the moment you are trying to leave a fight.
what you go there for
Every tree in the biome yields Boreal Wood regardless of which of the three shapes it grew into, and acorns planted on snow always come up boreal. Shiverthorn is the local herb and grows on both snow and ice. Underneath, the Ice biome holds Frozen Chestes and their gear, along with thin ice sheets over water that hold your weight until you land on them too fast.
Fishing here is unusually generous for how early you can do it. Frost Daggerfish are throwable weapons you can catch by the stack before your first boss, Frost Minnow makes Warmth Potions, and Atlantic Cod cooks into food. The biome crates, Boreal Crate and Frozen Crate, each guarantee one item from the Frozen Chest pool on top of their normal contents, which makes a fishing rod a faster route to that gear than hunting the chests underground.
hardmode raises it more than most biomes
Wolves and Ice Elementals start appearing at night, and blizzards can produce the Ice Golem, a slow giant whose frost beam chills you and can freeze you outright. Getting frozen with a wolf pack on you is how that encounter goes wrong.
Two drops make the biome worth farming. In Hardmode, anything you kill on snow or ice carries a 1/300 chance of yielding the Amarok, a yoyo strong enough to carry you through the mechanical bosses. The Frozen Key is far rarer at 1/2500 and opens the Dungeon's Ice Chest for the Staff of the Frost Hydra, though the chest stays sealed until Plantera is dead, so there is no rush on it.
it half resists the spreading biomes
Snow Blocks cannot be converted by anything. Ice Blocks can, turning into Purple Ice Block, Red Ice Block or Pink Ice Block depending on which biome reached them first. On the surface that means a snow region mostly survives Hardmode intact, since the ground there is largely snow. Below is a different story: the Ice biome is ice by definition, so the evil and the Hallow both run straight through it and start spawning Pigrons in their colors.
building one
A snow biome needs more than 1,500 snow or ice blocks, the heaviest tile requirement of any common biome and the reason artificial snow rooms are rare. If you only want the spawns rather than the music and water color, a single block will do, since snow plants and enemies appear on far less than the full count. Water never freezes on its own here either: every ice block in a world was placed during world generation, so an artificial biome has to be quarried out of the real one.
Two smaller quirks. Grass will not grow on dirt inside a snow biome, so a farm needs its blocks somewhere else. And if you have consumed the Torch God's Favor, biome torch swapping places Ice Torches automatically while you are here, which keeps the torch luck bonus working instead of quietly penalizing you for lighting the place with the wrong ones.