Place the plastic cups on a large tray or plate and set aside.
Place the candy canes into a plastic bag and seal. Crush the candy with a hammer or rolling pin. Set aside.
In a large mixing bowl, add the dry white chocolate pudding mix and cold milk. Whisk to combine.
Pour in the chilled peppermint schnapps and stir to incorporate.
Fold in the thawed Cool Whip and stir until well combined.
Spoon the pudding mixture into the plastic cups, filling each cup almost up to the top. Chill overnight or for at least 4 hours. After 4 hours, you can place lids on the plastic cups if not serving right away.
Before serving, add 1 Tablespoon of crushed candy canes on top of each pudding shot.