Special equipment: a 2-inch round pastry cutter; a piping bag fitted with a number 12 pastry tip; fun fake miniature Christmas trees, reindeer and sleigh and cowboy Christmas figurines to decorate the cake
For the red velvet crust: Adjust the oven racks to the middle and bottom of the oven and preheat to 350 degrees F. Spray a 13-by-9-inch metal baking pan with nonstick cooking spray. Place a double layer of parchment into the pan so that it overhangs the long sides; spray the parchment with cooking spray.
Add half of the cookies to the bowl of a food processor and pulse until the cookies resemble crumbs. Drizzle in half of the butter and half of the red dye, pulsing until it's all incorporated. Remove the first batch to a large bowl and repeat the with the remaining cookies, butter and dye. Combine both batches, then pour the cookie mixture into the prepared baking pan, using your hands to press the crust down to make one even layer. Bake for 10 minutes.
For the filling: Beat the cream cheese, granulated sugar and vanilla together in a stand mixer using a paddle attachment. Add the eggs one at a time, beating after each addition. Add the sour cream and mix again. Pour the filling over the crust and smooth the top.
Put a large roasting pan with water on the bottom rack of the oven and put the pan with the cheesecake on the top rack. Bake until the cheesecake is set and no longer jiggly, about 45 minutes.
Turn off the oven, open the oven door and allow the pan to sit in the open oven for 15 minutes. Remove and allow to cool for at least 2 hours. Once cooled at room temperature, refrigerate to chill for another 2 hours.
To assemble: Remove the cheesecake from the baking pan. Using a 2-inch round pastry cutter, carefully punch out 15 cheesecake circles. Remove them to a serving platter. Refrigerate while you make the mascarpone cream.
For the whipped mascarpone cream: Add the cream to the bowl of a mixer fitted with the whisk attachment and whip to stiff peaks. Add the mascarpone and confectioners' sugar and mix until well combined and smooth. Transfer the mixture to a piping bag fitted with a number 12 pastry tip.
For the Santa hats: Pipe a rim of the mascarpone cream around the top of each cheesecake circle. Put an inverted strawberry into the center of each and top with a tiny blob of the mascarpone cream. Chill to set.
To assemble the snow scene: Arrange the Santa hats on a cake stand, place the miniature Christmas trees, reindeer and sleigh and cowboy Christmas figurines around and dust with confectioners' sugar snow.