To take part in the Snowball Fights, talk to a tourist named John Frost. He usually walks along the coast in winter, during the Fights.
Select John to open the Snowball Fights interface, where you can start a union battle or a random battle. You can also proceed to ratings and the Winter Store to see its assortment of weapons.
To start the fight, you need to have enough snowballs. The quantity of snow is displayed at the top of the screen in the Snowball Fights interface. You can replenish your supply by pressing the plus sign next to the snow bar or by waiting a while for it to restore automatically.
If you have enough snow, press the button under the "Random Battle" section. It may take a while to find other players for the team. When all the players are found, the battle will start automatically.