The remake of the Summoner’s Rift took the better part of a year to implement, and the understanding had been that replacing the map with a winter-themed version would require the same amount of work for something only available briefly. However, a new procedure allowed the team to isolate specific portions of the textures, which allowed for a quick illusion of snow that took weeks, not months. You can see the process in short just below and read about the whole journey on the official site.
Source: Official Site