From Nookipedia, the Animal Crossing wiki
Snow people are special visitors that can be created with two snowballs during the winter season. Each day, two or three snowballs appear randomly throughout town (usually in different locations). They have to be the correct size in order to build a snowman; the head should be roughly three quarters as big as the body.
Snowballs increase in size when pushed on the snow, and decrease in size when pushed over non-snowy terrain. Initially, snowballs are difficult to push, but once they get to a certain size they become more controllable. If a snowball falls off a ledge, contacts a wall or body of water, gets hit by a shovel or axe, or falls in a hole, then it will despawn. A new snowball appears after entering a building.
Animal Crossing: City Folk and earlier
From December 25th to February 15th in Doubutsu no Mori e+ and earlier, December 10th to February 25th in Animal Crossing: Wild World and Animal Crossing: City Folk, players can create the snowman by pushing two snowballs together. The snowman will state if the job was perfect, good, average, or poor. The snowman's personality is determined by how it is made. For example, a poor job leads to the snowman's saying bad things about its life such as, "I just want to make one light shine before I melt away, oh woe is me." A perfect snowman rewards the played a snowman-themed item from the Snowman Series in the mail after the snowman melts. Additionally, the snowman also asks the player to build it a snow-lady. This unaffects receiving furniture.
In Doubutsu no Mori, Doubutsu no Mori+, Animal Crossing and Doubutsu no Mori e+, a snowman that has been built can be destroyed by the player by walking or running into it for about two seconds. During that time, the snowman's head rolls around and the head rolls faster until the snowman breaks apart. The speed of its head rolling around indicates how much closer it is to being destroyed by the player. However in Animal Crossing: Wild World and later, it was no longer possible to destroy a snowman (or snow person in Animal Crossing: New Leaf and later), since walking or running into it has no effect.
In Animal Crossing: City Folk, if a snowman is built anywhere on the pavement in front of the Town Gate, even out of the bus's path, the player will not be able to go to the city because the bus cannot stop.
Four different types of snow people can be built. From largest to smallest, they are Snowman, Snowboy, Snowmam, and Snowtyke. If built perfectly, they will shower the player with compliments and may offer special requests.
Snowballs can be found anywhere in town from December 11th to February 25th. The snow people that were made the last few days before the snow on the ground melts will still be present, but they will mention about how warm it is getting or say that they hope for the player to build them next winter.
Each day in Animal Crossing: New Leaf after any snow people are built, they will melt a bit around the body until the 4th (and final) day is when the snow person's body is almost fully melted, and their head is almost on the ground. After the 4th day, the snow person disappears from the town, since the snow person has fully melted. Unlike previous games, they melt more realistically instead of just shrinking.
Snow people can also be called using the megaphone.
Each snow person has a different kind of personality and voice.
Snowman plays bingo with the player and if the player is lucky, a Bingo is scored and the player wins a winter sports series furniture as a prize in exchange for the completed bingo card. A Snowman has the same voice as a cranky villager.
A perfect Snowboy mails the player Snowman themed furniture. A Snowboy is the same as the Snowman from Animal Crossing: City Folk and earlier, the only difference being the name. A Snowboy has the same voice as a lazy villager.
Snowtyke yearns to be reunited with the snow people family, and building the other versions will allow Snowtyke to mail special furniture. A Snowtyke has the same voice as a peppy villager.
Snowpeople appear as a collectible trophy.
Name in Italics indicate PAL trophy name.
Names in other languages
Snowman (Doubutsu no Mori, Doubutsu no Mori+, Animal Crossing, Doubutsu no Mori e+, Animal Crossing: Wild World and Animal Crossing: City Folk)
Snowman (Animal Crossing: New Leaf)