Snow

Snow was a form of precipitation; similar to rain, though when the atmospheric temperature is below the freezing point of water, the result is snow. Other than Earth, snow was known to fall on other planets, including Gallifrey, Sto and Ood Sphere. The Doctor was known to be fond of snow. (DW: Gridlock, Voyage of the Damned, Planet of the Ood)

Fake snow
In his tenth incarnation the Doctor, encountered many instances of snow that wasn't snow at all;
 * During Christmas Day, 2006 the "snow" falling on London was in fact ashes from the remnants of the Sycorax space ship that was destroyed by the Torchwood Institute, on Harriet Jones' order. (DW: The Christmas Invasion)
 * During Christmas, 2007 the tenth incarnation of the Doctor used his TARDIS to excite the atmospheric conditions around London to create snow. (DW: The Runaway Bride)
 * On Christmas Day, 2008 the ballast from the spaceship Titanic went through the atmosphere, where reentry resulted in another instance of falling ash that resembled snow. (DW: Voyage of the Damned)

Real snow

 * In Cardiff in 1869 during Christmas it snowed. (DW: The Unquiet Dead)
 * The Doctor commented with glee "snow, real snow." when he arrived on Ood Sphere in 4126. (DW: Planet of the Ood)
 * Upon arriving in 1851, London; at Christmas, the Doctor was very pleased with encountering the actual snow. (DW: The Next Doctor)
 * In 2059, the Doctor was happy to see snow on Earth after bringing the remaining crew of Bowie Base One back from Mars. (DW: The Waters of Mars)

Other Appearances

 * DW: Marco Polo
 * DW: The Keys of Marinus
 * DW: The Tenth Planet
 * DW: The Ice Warriors
 * DW: The Seeds of Doom
 * DW: The Ribos Operation
 * DW: The Unquiet Dead
 * BFA: The Magic Mousetrap
 * MA: Cold Fusion
 * NA: Timewyrm: Revelation
 * PDA: The Wages of Sin
 * PDA: Drift
 * NSA: The Krillitane Storm
 * TN: Time and Relative

Behind the Scenes
One of the deleted scenes for The Waters of Mars showed the Doctor expressing his love for snow and Yuri Kerenski telling the him that it's the Carbon Wash cleaning the atmosphere and questioning him because he doesn't know this fact. Whether this fact is still supposed to be seen as part of the episode is unclear and it is also unclear as to whether this is still real snow with a new scientific name or a process which is unknown.