To unlock the Get Your Snowshoes Ready trophy in Cities: Skylines, you will need to purchase and install the Snowfall DLC.
Once installed, start a game on one of the three Winter maps: Snowy Coast, Icy Islands or Frosty River. You don't have to build anything on the map (although you will need to for other trophies in the DLC). After around 10-15 minutes you should see snow for the first time, although it does appear to be random when it actually begins to snow.
Once it snows in game, the trophy will unlock.